Math and Logic Puzzles

Math, Science, and Investing

2012-01-24T23:44:00.001-06:00

These days it's not only business majors who get jobs on Wall Street. A lot of people from math and science backgrounds are also hired.

They are used on both the trading side (to come up with systems that can make money), as well as investment banking.

For example, a firm called the Valence Group is involved in chemical investment banking.

They leave investment banking for other businesses to other Wall Street players.

Instead, they hired and developed expertise in chemistry and chemical engineering. These fields are valuable in chemical m&a advisory and chemical mergers and acquisitions deals, because their people would know, for example, if certain types of chemical factories can be combined to achieve cost savings.

Certain transactions may look good on paper but fail due to technology. Only someone with the proper math and science background would be able to pick it up.

On the other extreme, someone with the proper background may see opportunities for economy of scale and reducing costs that other groups don't see. This would give Valence Group's clients a competitive advantage that would let them bid higher.

The Boy and The Store Keeper (The Power of Compound Interest)

2012-01-24T23:00:00.001-06:00

A boy went to his neighborhood store and asked to work for 1 month. He offered to work the first day for a penny, as long as it was doubled each day.

The amused shopkeeper agreed, and even signed a contract.

Well, of course, the boy ended up owning the store! The boy's pay on the last day of the month (31th day) was $10,737,418.24!

Such is the power of compounding.

Mathematically, we can describe compounding as multiplying the starting amount by (1 + interest rate/100) raised to the number of time intervals.

For example, $100 compunded at 10%/year for 3 years would be:

100 X 1.10^3

In the boy's case, we would calculate his pay for any given day D as:

0.01 X 2^(D-1)

(We use D-1 because the figure is calculated for the day, not for the end of it).

So, on day 1, the boy gets 0.01 X 2^0 = $0.01.

On day 4, the boy gets 0.01 X 2^3 = $0.08

On day 10, 0.01 X 2^10 = $10.24, and so on.

Roots and Powers

2012-01-24T22:59:00.001-06:00

Raising a number to a power P means multiplying the number by itself P times.

It is usually denoted with the symbol ^ or **.

For example,

3^0 = 1

3^1 = 3 = 3

3^2 = 3*3 = 9

3^3 = 3 * 3 * 3 = 27

3^4 = 3 * 3 * 3 * 3 = 81

Raising any number to 0 is always defined as 1.

When you use ^2 it is called squaring, and ^3 is calling cubing.

The opposite function is called finding the root. It means taking a number n and a root r, and returning the number that, if raised to power r, will give n. The symbol is hard to show on the computer, so, for a moment, we will just call it rootr().

For example,

root1(3) = 3

root2(9) = 3

root3(27) = 3

root4(81) = 3

Now, just like subtraction is adding a negative number, and dividing is multiplying a fraction, roots can be expressed as raising to a fractional power.

So,

3^(1/1) = 3 because 3^1 = 3

9^(1/2) = 3 because 3^2 = 9

27^(1/3) = 3 because 3^3 = 27

81^(1/4) = 3 because 3^4 = 81

Great Trip

2012-01-19T23:06:00.002-06:00

Guest post written by Joseph Finch

I visited http://www.directstartv.com/ and decided that I was going to upgrade our television package. My husband and I have finally saved up enough money to plan our dream trip to Europe. We have a whole month ( we are professors) that we are going to be able to travel. I have been watching every travel show that I can and been taking notes. I have planned a trip where we fly into London. We are going to travel around Europe the whole time. There are a few things that we are dying to see and were put at the top of the list. We both really want to go to Switzerland. We also want to make it to Paris ( the city of love), Normandy beach, and the Vatican. There is also a lot of room in between for us to go some smaller and less touristy places. I have also been doing a lot of research on the internet and booking part of the trip through the internet. We just can’t wait! It is going to be awesome!

Candles Problem

2012-01-19T23:05:00.001-06:00

This is from the 12/16/2007 "Ask Marilyn" column in Parade magazine:

I have two candles, one an inch longer than the other. I light the longer one at 3 pm and the shorter one at 5 pm.

At 9 pm, they're the same length.

The longer candle goes out at 11 pm, and the shorter one goes out at 10:30 pm.

How long were they at the start?

Please click here for the answer.

HourGlass Puzzle

2012-01-19T23:04:00.001-06:00

This is also from the AskMarilyn column in the December 2, 2007 Parade Magazine:

Your rich uncle dies, and you're in his will. From his collection of timepieces, he leaves you the 7-minute hourglass and the 11-minute hourglass.

To honor his memory, you open a reflexology salon and use the hourglasses when you give foot massages. But your clients want 15-minute massages instead.

How do you use your cherished timepieces and still manage to please your clients?

Please click here for the answer.

"Cloud" Accounting for Small Businesses

2012-01-17T23:50:00.000-06:00

Most of the "cloud" applications I hear about are aimed at individuals or large companies. Also, the applications tend to be in areas such as sales, marketing, or storage.

But, recently, I read about a company called Outright.com that offers online accounting and bookkeeping software for small businesses.

I think we will see many more small business and financial applications in the cloud because it's a win-win situation for both the vendor and the customer.

For the vendor, they save on the costs of packaging and distributing their software, as well as customer support issues due to installations and customers with different versions of the software.

For small business customers, they don't have to deal with installation, hardware, and operating system requirements. They will always have access to the latest versions and patches. Finally, they can depend on the vendor for security, backups, etc. which would consume a lot of resources at a small company.

Monte Hall Logic and Probability

2012-01-17T23:43:00.001-06:00

I've read about the Monte Hall Problem in a few different places.

Basically, the situation is that you are on a game show, and there are 3 doors in front of you. There is a car behind one door, and goats behind the other two. If you pick the door with the car, you win the car!

So, you pick one of the doors. Now, at this stage in the game, the host always opens one of the two remaining doors, which always has a goat behind it.

Now, there are only two doors to choose from. The host now gives you the chance to either stay with your choice, or switch to the other door.

What should you do?

The answer, which generates some controversy, is to always switch, because there is a 2/3 chance that the car is behind the other door. A lot of people think the odds are 50-50, but this isn't so.

When you first picked your door, there was a 2/3 chance that the car was not behind the door you picked. For convenience, let's say that you picked door A, and the other two doors are B and C. So, there is a 2/3 chance that the car is behind B or C.

Now, the host opens door B. The key is that, when the host chooses a door to open, he always chooses a door with a goat behind it. That means the host knows where the car is, so his choice is not random. This is why there is still a 1/3 chance that the car is behind door A and a 2/3 chance that the car is behind door C.

I read somewhere that this problem is easier to understand if we consider more doors. So, let us say that there are 100 doors. The car is behind one of the doors. You pick your door, and then there is a 99/100 chance that the door is behind one of the other 99 doors.

Now, the host opens 98 of the doors, revealing goats. So, now you are down to 2 doors: the one you picked and the one that the host did not open. Now, it should be a little easier to see that there is a 99/100 chance that the car is behind the second door, and that you should switch.

In both cases, the second door survived a "test" of the host unveiling goats, while your initial choice was never subjected to a test.

Secured Data Sites For Sharing Confidential Financial Data

2012-01-06T00:34:00.000-06:00

I'm always interested in specialized niche businesses that are successful by doing one thing really well - something that the general public probably doesn't even realize is a genuine need.

Recently, I came across a specialized business which is related to trading and Wall Street.

The business is called Merril DataSite, and they provide Virtual Data Rooms for capital market / financing functions such as mergers and acquisitions (M&A) activities, business ownership transfers, bankruptcies, restructurings, licensing activities, etc.

Basically, their data sites are useful for any firms that are involved in complex business, financial, and/or legal processes that involve sharing highly confidential documents (such as professional VDR solution for IPO process) between groups of financial analysts, lawyers, and / or accountants.

A secure data site process can insure that the documents stay protected from outsiders by limiting access to only authorized individuals, and keeping track of checkouts and revisions.

In an interesting extension of their business, a division of Merrill called Merrill Brink translation services is a technical translation services provider for international clients.

Elegant Simplicity and Power of the Google Search Bar

2012-01-06T00:27:00.002-06:00

The Google home page search box is a great blend of minimalism and power. It provides a simple command-line interface to a powerful, behind the scenes network.

The "search" box allows you to do more than just search for web pages:

1. It is a full calculator - just enter a math equation like (34+23)*7 to get the result.

2. Tracks packages - simply enter a USPS, UPS, or Fed Ex tracking number.

3. Find a theater and show times - enter the movie name and zip code, i.e. "iron man 2 10022".

4. Flight information - simply enter the airline and flight number.

5. Sports results - just type in the name of a team.

6. Government websites - search them by going to google.com/unclesam

7. Currency conversions - enter a phrase like "dollars in rupees" or "USD in INR" or "100 dollars in pounds".

8. Search within a website - i.e. "Iraq cnn.com" searches CNN for Iraq.

9. Time zones - i.e. "time Moscow"

10. Conversions - examples include "10 teaspoons in ounces", "meters in feet", "cups in gallons".

Math Tutoring for Elementary Students

2012-01-06T00:24:00.001-06:00

A mathematics education is a fundamental skill that all children need to learn. Today, a good grounding in math is a requirement for a lot of good jobs - such as programming, machine tools, science, engineering, etc.

As the U.S. Secretary of Education said: "To compete in the global economy, you must know math."

If your child is having trouble with math, you might want to get him or her help through an elementary math intervention program. They can help with all levels and subjects in math - including artithmetic, geometry, pre-calculus, etc.

Services for an elementary math intervention program can help children either through individual programs or through small groups - whatever method is more effective for your child.

Also, they tend to use "virtual manipulatives" (online animation, objects, and word problems) to reinforce concepts.

What is the Chance That The Patient Has The Disease?

2012-01-06T00:10:00.002-06:00

I read Nassim Nicholas Taleb's book "Fooled by Randomness", and he gave an interesting example of a mistake in calculating probablities:

A test for a disease has 5% false positives (This means that 5% of the tests given to those who do not have the disease come back positive - so if 100 people test positive, only 95 actually have the disease). The disease strikes 1/1,000 of the population. People are tested at random, regardless of whether they are suspected of having the disease. A patient tests positive. What is the probability of the patient having the disease?

Please click here for the answer.

Enjoying Sudoku Logic Puzzles

2012-01-06T00:07:00.001-06:00

I enjoy solving Sudoku puzzles. In the last decade, Sudoku has grown to rival crossword puzzles in popularity.

A Sudoku puzzle consists of a 9x9 grid with nine 3x3 mini-grids. The 81 boxes need to be filled in with the digits from 1 to 9. The trick is that all 9 numbers must be used once and only once in each row, column, and mini-grid. A few of the numbers will already be filled in for you.

Sudoku is pure logic - there are no calculations involved.

Sudoku is available in all the major newspapers and in books. I even once got an electronic Sudoku device as a gift. Amazon has a lot of Sudoku books and merchandise.

Specializing in Taxation

2012-01-05T23:58:00.000-06:00

The tax code is so complex that CPAs and lawyers can build a career just specializing in taxation.

In fact I recently found a website (FastForwardAcademy.com) that found a need for tax professionals who want to continue their education and become certified in tax preparation.

They provide study guides, practice tests, and other study material for passing the tax preparer certification exam.

Accountants and other tax professionals are willing to study for and become Registered Tax Return Preparers
because this designation / specialization will let them stand out from their competition.

Find The 9-Letter Word

2012-01-05T23:49:00.001-06:00

There is a 9 letter English word such that, if you remove one letter at a time, it will always be a word.

Thus, it can be a 9 letter word, 8 letter word, etc. down to a 1 letter word.

What is this word?

Please click here for the answer.

Finding The Interest Rate

2012-01-05T23:47:00.002-06:00

In a previous Unix blog post, I gave two awk scripts for calculating compound interest.

Now, let us look at the opposite problem. If we have a starting amount and ending amount, after X number of time periods, what is the average interest rate per time period? We can use awk.

For example, If we started with $4000, and had $5200 after 6 years, what interest rate did we average per year?

We can use:

nawk 'BEGIN {print (5200/4000)^(1/6)}'

to get an answer of 1.0447. So, we made about 4.5% a year for 6 years.

In this case, we are using the math principle that raising something to 1/N is like taking the Nth root.

So, 4000* 1.0447^6 = 5200.

This is covered in my powers and roots post on my math and logic blog.

Simple, Math Oriented Business Due to The Complexity of the Tax Code

2012-01-03T00:35:00.000-06:00

As an analytical person who values simplicity and minimalism, I I like to see businesses that succeed by finding a simple need, and then filling it.

In this case, it is a need for tax preparers to prepare returns - due to the complexity of the tax code.

FastForwardAcademy is dedicated to providing tax preparer exam courses to help people enter this field.

They also provide study guides, practice tests, and other study material for passing the irs exam to become IRS certified enrolled agents.

Accountants and other tax professionals are willing to study for the enrolled agent certification because it will let them stand out from the competition.

Chance of Having Two Boys

2012-01-03T00:31:00.001-06:00

This was a question that generated controversy in Parade Magazine's "Ask Marilyn" column back in 1996.

The question was:

Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

Please click here for the answer.

Can You Get 24?

2012-01-03T00:30:00.001-06:00

Note: This puzzle is from MathIsFun.com:

How can you get the answer 24 by only using these four numbers: 8, 8, 3, 3 ?

You can use the main functions: add, subtract multiply and divide.

Please click here for the answer.

BizzClick

2011-12-31T19:05:00.001-06:00

If you are into math and the internet - especially creating websites, blogs, etc. - you have probably heard of pay per click advertising.

This is a win-win form of advertising where the advertiser pays the website owner (publisher) a small amount of money each time a reader clicks on a link in an ad to go to the advertiser's site.

It is a win for the advertiser because they only pay when a potential customer takes the initiative of clicking a link. This means that they are only paying for traffic that is more targeted, and more ready to buy - because someone not interested at all in the offer would not bother to click.

It is a win for the publisher (web site owner) because, instead of charging a subscription or fee to give out information, he or she can attract a bigger audience because they are giving their information away free, while getting paid from the actions of their readers who are genuinely interested in the offer.

If you are interested in pay per click advertising, either as an advertiser or publisher, you might want to check out BizzClick.com. They have a 24/7 support team, and they create tools and alogrithms (such as their FiSoAp system) to help advertisers and publishers extract maximum value while cutting down on charge backs and invalid clicks.

How Long Are The Candles?

2011-12-31T18:51:00.004-06:00

Introduction to Roots and Powers

2011-12-31T18:51:00.002-06:00

Raising a number to a power P means multiplying the number by itself P times.

It is usually denoted with the symbol ^ or **.

For example,

3^0 = 1

3^1 = 3 = 3

3^2 = 3*3 = 9

3^3 = 3 * 3 * 3 = 27

3^4 = 3 * 3 * 3 * 3 = 81

Raising any number to 0 is always defined as 1.

When you use ^2 it is called squaring, and ^3 is calling cubing.

For example,

root1(3) = 3

root2(9) = 3

root3(27) = 3

root4(81) = 3

Now, just like subtraction is adding a negative number, and dividing is multiplying a fraction, roots can be expressed as raising to a fractional power.

So,

3^(1/1) = 3 because 3^1 = 3

9^(1/2) = 3 because 3^2 = 9

27^(1/3) = 3 because 3^3 = 27

81^(1/4) = 3 because 3^4 = 81

Scholarship Info Site

2011-12-29T23:53:00.000-06:00

Since readers of this blog tend to be interested in education, I though I would mention about a website that provides free financial aid information, including info on scholarships.

This website is designed in a minimal, simple, and focused style that makes it easy for a visitor to search and locate the right scholarship for him or her.

From the main menu here, a site visitor can easily branch out with one click into sub topics such as engineering grants or scholarships for left handed students.

Euclid's Game and Greatest Common Divisor (GCD)

2011-12-29T16:41:00.001-06:00

I found a new math puzzle website called Cut-the-Knot.org. They have an interactive puzzle called Euclid's Game.

In this game, you start with 2 random positive numbers. Then, the players take turns. They have to write down a positive number that is not already on the list, and that is the difference between any two numbers already on the list. When someone can't make another move, the game is over.

For example, if the list is 4,16 then the only additional number is 12. Then, with a list of 4,16,12 you could add 8. Then, the game is over.

This is related to Euclid's algorithm. In this case, the greatest common divisor (gcd) of 4 and 16 is 4. So, the only possible differences are multiples of the gcd between up to 16. Thus, the only differences are 4,8,12.

Thus, if the two numbers were 32 and 56, then the gcd is 8, and the possible differences are 8, 16, 24, 32, 40, 48, and 56.

Getting An Online Education

2011-12-17T01:46:00.000-06:00

A great gift of self-improvement you can give yourself is to go back to school and learn something new - either for personal enrichment or to start a new career.

As an alternative to physically taking a class, you might want to explore online learning. It is a cheaper option (http://www.onlinedegree.com/infographics/true-cost-college) that is becoming a lot more popular than only a few years ago (http://www.onlinedegree.com/infographics/growth-online-learning). Online education also has the advantages of wiping out geographical distances and making it easier to juggle work and family obligations.

http://www.onlinedegree.com is one of the better search portals that let you search for accredited online degrees, schools, and courses. Using this specialized search tool is much more efficient than researching schools through a general search engine - you won't get results unrelated to education, and you can easily limit the domain over which you search, so that your search is tight and efficient. For example, if you are interested in studying to be a medical technologist, you can confine your education search to online degree programs in healthcare.

Summing Integers

2011-12-17T01:37:00.003-06:00

A neat fact is that the sum of integers from 1 to N is equal to N * (N+1) / 2.

So, for example, 1+2+3+4+5 is equal to 5*6/2, which is 15.

This fact is really useful if you want to sum huge strings of consecutive numbers, because no matter how many numbers you have, this formula will give you the answer in one calculation.

So, if you actually added up the integers from 1 to 10,000 it would require 10,000 additions. But, you can easily calculate the sum with one calculation: 10000*10001 / 2. which equals 50,005,000.

Thus, a programmer who codes the formula, instead of using brute force addition, would create a program that would run instantaneously, even for adding up millions of integers.

Here is an awk script for summing the integers, which I posted on my unix blog.

Students At The Zoo

2011-12-17T01:37:00.001-06:00

I saw the following problem in the "Ask Marilyn" column in Parade Magazine. It is a good example of problem solving involving groups:

Say 90 students go to a zoo. Three have a hot dog, soda, and Popsicle; 24 have a hot dog; five have a hot dog and soda; 33 have a soda; 10 have a soda and Popsicle; 38 have a Popsicle; eight have a Popsicle and hot dog. How many had nothing?

Try to answer this problem for yourself. Then, you can click here to see the solution and analysis.

No More Office TV

2011-12-17T01:32:00.000-06:00

Posted by Hyman Weeks

We used to have a TV in the office above my desk and I would sit there and watch Ina Garten and everything else on the Food Network all day long. One day without warning they took it away from me and that’s when I decided to just go for it and get it at home, too. I got direct tv austinand man, now I watch so much TV – it’s probably not good for me! I don’t feel too bad watching stuff on cooking because I feel like I’m learning and I know that at the end of the day it’s not rotting my mind or whatever it is people say. There’s something soothing about watching someone else cook and though I can’t actually taste the food they make I think it just all looks delicious (I think they use colored lenses or something.) Anyway, I don’t know that I’m actually a better cook now than I was but I surely know some techniques and dishes I had never heard of before now!

Going To Work Puzzle

2011-12-14T16:30:00.001-06:00

A man jumps in his car and leaves for work, driving at 30 mph.

Half and hour later, his wife realizes that he forget some important papers he needs.

She jumps into her car with the papers and drives after him at 60 mph.

How long does it take for her to catch up to him?

Please click here for the answer.

Egg Timing Puzzle

2011-12-10T13:28:00.000-06:00

You want to boil eggs for exactly 9 minutes, but only have two hourglasses: a 4 minute hourglass and a 7 minute hour glass.

How do you determine when exactly 9 minutes have gone by?

Please click here for the answer.

Metal Detecting: A Hobby Involving Mystery, History, and Potential Treasure

2011-11-25T00:57:00.000-06:00

People who love metal detecting share a lot of traits with those of us who like math and logic puzzles: They like to systematically explore concepts, and are curious about solving mysteries and challenges. They get excited by making surprising discoveries.

Serious metal detecting hobbyists invest in sophisticated and high quality Metal Detectors from suppliers such as JoanAllen.co.uk.

They buy detectors that suit their needs. For example, hobbyists might want a good quality detector that can work in most environments (sand, shallow water, land, etc.), while someone more professional and/or on a more specialized adventure (such as looking for antique coins or jewelry, or ancient archeological specimens) might want a deep penetrating detector that can weed out false readings - such as those from nails, screws, etc.

Math Puzzle: Chance of Having Two Boys

2011-11-25T00:36:00.003-06:00

This was a question that generated controversy in Parade Magazine's "Ask Marilyn" column back in 1996.

The question was:

Say that a woman and a man (who are unrelated) each have two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

Please click here for the answer.

Can You Generate 24?

2011-11-25T00:35:00.001-06:00

Online Computer and Software Training for Continuing Education

2011-11-17T23:10:00.000-06:00

Many readers of this blog are either working in, or preparing for, a career in math, science, or engineering.

As I have found over the last 21 years (since I graduated college), your career will be fun, interesting, challenging, and well-paid.

However, technology will keep changing at an ever faster rate, and you will have to be a perpetual student and keep learning.

Unlike high school or college, however, you will now mostly take Computer Training courses online, at your own pace. You will have to become self-motivated, and good at balancing work, family, and continuing education.

CBTraining.com is a site that provides online IT training classes. Their site has the advantage that you can browse through their course offerings based on the software package, certification desired, or by the type of industry.

The site also ranks computer courses based on popularity. This lets you leverage the knowledge and experience of your peers to help you identify the most valuable classes that will help advance your career.

In my experience, the return on investment for IT and computer courses is very high. They are almost never a waste of your time.

The Colors of Their Skins - The Answer

2011-11-17T22:11:00.000-06:00

(Solution Hidden)

None of the aliens have the same skin color as their names, thus Mr. Red is not red.

But Mr. Red is not green either, since the alien with green skin responds to his statement.

Thus, Mr. Red is blue, Mr. Blue is green, and Br. Green is blue.

The Colors of Their Skins

2011-11-17T22:05:00.002-06:00

This is a logic puzzle courtesy of Brainden.com.

On the planet Phosphoron there are beings of three skin colors, red, green, and blue. Three beings, Mr. Red, Mr. Green, and Mr. Blue were discussing the beauty that this variety gives to Phosphoron.

"I think it's interesting," says Mr. Red, "that none of the three of us has the skin color that our names would suggest."

"Who the heck cares?" replies the fellow with green skin.

What color skin does Mr. Green have?

Please click here to get the answer.

FastForwardAcademy.com - Example of Simple, Successful Website Forcusing On One Thing

2011-11-11T14:29:00.000-06:00

"Stock Trading Riches" is now available in Kindle format on Amazon.com

2011-11-10T15:05:00.001-06:00

My book "Stock Trading Riches" is now available in Kindle format on Amazon.com.

Since this is a new format, it's priced for now at $2.99.

They did a good job in the conversion - I saw that the stock tables and programming scripts display well, and the links are click-able.

You don't need to own a Kindle to buy this edition. You can download free readers for PC's, Mac's, iPads, etc.

More Halloween Fun

2011-10-31T08:04:00.001-05:00

Ben and Jerry's Halloween interactive website:

http://www.benjerry.com/halloween/

Happy Halloween!

2011-10-31T00:43:00.002-05:00

I publish this link on my blogs every year at Halloween time, it's pretty cool:

http://ak.imgag.com/imgag/product/preview/flash/bws8Shell.swf?ihost=http%3A%2F%2Fak.imgag.com%2Fimgag&brandldrPath=%2Fproduct%2Ffull%2Fel%2F&cardNum=%2Fproduct%2Ffull%2Fap%2F3125133%2Fgraphic1

Money Problem - The Answer

2011-10-20T23:42:00.000-05:00

(Solution Hidden)

We have three equations with three unknowns, so we can make substitutions and solve the problem.

If we let D = Doug, B = Bill, and S = Steve, we have:

D = 6 * S

B = 3 * S

D + B + S = 550

After substituting the first two equations into the third, we get:

(6 * S) + (3 * S) + S = 550

10 * S = 550

S = 55

Thus,

D = 6 * 55 = 330

B = 3 * 55 = 165.

So, Doug has $330, Bill has $165, and Steve has $55. These three amounts add up to $550.

Money Problem

2011-10-20T23:36:00.001-05:00

Doug has 6 times as much money as Steve.

Bill has three times as much money as Steve.

Together, Doug, Bill, and Steve have $550.

How much money do each of them have?

Please click here for the answer.

Will We Own Music In The Future?

2011-10-20T22:57:00.001-05:00

I was recently reading an article about predictions for the future, and it covered the usual stuff about land lines, CD's, and books disappearing and becoming obsolete.

But, the idea that caught my attention was about how the definition of owning something might change - specific examples include music and software.

Because, in the future, we may not keep these on our MP3 players or computers. Instead, music and software will probably reside in the "cloud" - meaning stored on some companies servers far away - accessed transparently over the internet.

I that is the case, can we say that we own the music or software? I guess, if we uploaded it or paid for it independently, it is ours. On the other hand, what if we just pay a monthly "all you can eat" fee, and stream the music or software from a generic location on the cloud - not from a directory assigned to us?

In that case, do we "own" anything?

Age and Time Problem - The Answer

2011-10-11T22:43:00.000-05:00

(Solution Hidden)

We can let F stand for Fred and S for Samantha.

Then, we know that Fred is 8 years older than Samantha, so
we have F = S + 8

Second, we know that, in three years, Fred will be twice Samantha's age. Fred's age in three years is F+3, while Samantha's is S+3.

So, we have a second equation: F + 3 = 2 * ( S + 3 )

We can substitute the first equation into the second to solve the problem:

(S+8) + 3 = 2 * (S + 3)

S + 11 = 2S + 6
5 = S

So, Samantha is 5 years old. By substituting this into the first equation, we get:

F = 5 + 8 = 13

So, Fred is 13 years old.

This works, because, in three years, Samantha would be 8 and Fred 16, which is twice her age.

Age and Time Problem

2011-10-05T22:33:00.008-05:00

Fred is 8 years older than his sister Samantha.

In three years, he will be twice as old as her.

How old are Fred and Samantha?

Please click here for the answer.

Word Problem

2011-09-27T23:35:00.000-05:00

Car #1 leaves San Francisco at 9 am and heads for Denver at 50 mph.

Car #2 leaves Denver at 11 am and heads for San Francisco at 60 mph.

The cities are about 1200 miles apart.

When the cars meet, which one will be closer to Denver?

Click here for the answer.

Magic Lily Pond Puzzle

2011-09-27T23:33:00.002-05:00

Note: This puzzle comes from the book Brain Teasers by Kiran Srinivas.

In ancient Egypt, there are magical lily ponds. On these ponds, each flower doubles over night. For example, if a pond has one flower on a certain day, the next day there will be two flowers (both the same size as the original flower).

On March 1, you place a single flower on an empty magical pond. On the last day of the month, March 31, you return to find the pond's entire surface 100% perfectly filled with flowers. What was the first day on which the pond's surface was at least 30% covered with flowers?

Please click here for the answer.

My own business

2011-08-16T22:45:00.000-05:00

Author: Joseph Sandoval

When I decided to start my own business I never really imagined all that would have to go into. I didn’t think about things like getting a security system or adding another few lines to the phone – it all added up over time! I also hadn’t really considered furniture for the lobby or how expensive it would be or the satellite for the plasmas I planned to run. That was an easy fix, though, when I went to ExpertSatellite.com and got a good deal, as was the furniture once I talked to my brother who’s a designer. Anyway, over time it all added up and I’m about a year after opening now and about to break even if my calculations are correct. Who would have guessed you’d have to think about things other than rent and paying employees? I guess when it came down to it I wasn’t really set up to be a small business man from the get go – this career takes a lot of learning as you go!

Fruitful Problem - The Answer

2011-08-16T22:41:00.000-05:00

(Solution Hidden)

She picked the box with the label "apples and oranges".

There are two possibilities: she picks an apple, or she picks an orange.

If she picked an apple, then "apples and oranges" is really "apples". Now, since all the labels are wrong, it means that the box labeled "oranges" must be different. Since "apples" is already taken, it must be "apples and oranges". Then, the box labeled "apples" must be "oranges".

If she picked an orange, then "apples and oranges" is really "oranges". Now, since all the labels are wrong, it means that the box labeled "apples" must be different. Since "oranges" is already taken, it must be "apples and oranges".

Fruitful Problem

2011-08-16T22:10:00.001-05:00

This problem is from Steve Miller's Math Riddles.

There are three boxes. One has apples, one has oranges and the other has apples and oranges. The boxes are labeled wrong so that no label is correct. Sue opens just one box, and without looking in the box, takes out one piece of fruit. She looks at the fruit and immediately labels all the boxes correctly. Which box did she open and how did she know?

Please click here for the answer.

Simple and Elegant Website for A Complex Problem

2011-08-13T01:24:00.001-05:00

The tax code is so complex that CPAs and lawyers can build a career just specializing in taxation.

In fact I recently found a website that is dedicated to providing enrolled agent continuing education to help pass certification tests. I like small internet businesses that succeed by finding a simple need, and then filling it.

In this case, the website (FastForwardAcademy.com) found a need for tax professionals who want to continue their education and become certified in tax preparation.

They provide study guides, practice tests, and other study material for passing the enrolled agent ethics course to become IRS certified.

Accountants and other tax professionals are willing to study for and pass the ea cpe
because the enrolled agent certification will let them stand out from the competition.

Adding Up Consecutive Integers

2011-08-13T00:45:00.002-05:00

In the last post, I described a formula for calculating the sum of integers 1 to N.

Now, let's derive a formula for the more general case of summing the integers from M to N, where M <= N.

Well, we can write the Sum of M to N as: Sum(M,N) = Sum(1,N) - Sum(1, M-1)

So, for example, the sum of 5-6 would be the sum from 1-6 minus the sum from 1-4.

We know that the Sum(1,N) would be N*(N+1)/2. The Sum(1,M) would be M*(M+1)/2.

Then, the Sum(1,M-1) would be (M-1)*(M-1+1)/2, which simplifies to (M-1)*M/2, or

M*(M-1)/2.

Thus, the Sum(M,N) would be N*(N+1)/2 - M*(M-1)/2

So, the sum of 5-6 would be 6*7/2 - 5*4/2 = 21 - 10 = 11

Now, we can calculate the sum of any series of consecutive integers - even 5 to 10 million - in one step.

This is an example of simple elegance over brute force.

Jelly Bean Puzzle

2011-08-13T00:44:00.002-05:00

In a bowl of jelly beans, all but 16 are red, all but 16 are green, all but 16 are blue, and all but 18 are yellow.

How many of each color are in the bowl?

Please click here for the answer.

Search Engine For Online Education

2011-07-20T22:34:00.000-05:00

Since many of my readers are interested in education, I thought I would mention about a search portal called FindYourEducation.com that specializes in finding Online Schools for continuing your education.

I like websites that come up with useful, specialized niches to serve. A search engine for online education is very useful because it saves time, letting you locate college and degree information quickly while avoiding web pages that are not education related.

You can narrow your search to focus on a particular school, or a particular subject, such as online degree programs in game design.

This engine can also refer you to useful education related sites such as http://www.fafsa.ed.gov/ - where you can Free Application For Federal Student Aid.

Using a search engine like this, you should take your time and really explore your options, because online education has exploded, and you have a lot more alternatives than even from 5 years ago.

The whole spectrum runs from private schools that only offer online degrees, to traditional colleges that offer degrees completely online, all the way to programs that require you to take a semester, or even 1/2 the degree physically on campus.

Personally, I think that having to attend some real life classes can enhance your experience but, should be thought of as optional. If making physical appearances causes problems with watching children, spouses, work, etc. Then you should look ito completely online degrees.

Who Is The Oldest? - The Answer

2011-07-20T14:39:00.001-05:00

(Solution Hidden)

Statement #2 tells us that Claude is not the oldest.

So, the oldest is Marie or Jean.

From statement #3, Jean has the sum of Claude and Marie's points.

If Jean was the oldest then, by statement #2, Claude would have 1/2 his points. But that means that Marie would also have 1/2 his points.

This contradicts statement #1, which says that the youngest has the fewest number of points.

Thus, Marie is the oldest.

Who Is The Oldest?

2011-07-20T14:30:00.001-05:00

This puzzle is by Caroline Latham at SharpBrains.com.

Marie, Claude, and Jean are in a competition. Here are their results:

1. The youngest person received the least points.
2. Claude got half of the points of the eldest.
3. Jean received as many points as both others combined.

Who is the oldest ?

Please click here for the answer.

Gold Bullion Investing

2011-06-17T17:30:00.000-05:00

As a passionate advocate of simplicity and minimalism, I love websites that do one thing very well. A strong example of this type of site is GoldCoinsGain.com, which specializes in bullion and gold coin investments.

The site does not write about other investments (i.e. stocks or real estate) - just how to buy bullion. It is apparent that this site's author is an expert on gold bullion investing, and his passion for the site is very evident. This site contains knowledge that I have not seen on more general financial sites.

For example, who knew that you could save for retirement with a gold IRA? This site contains detailed information on the subject of learning how to buy gold bullion.

Monte Hall Probability Paradox

2011-06-17T17:09:00.002-05:00

Benford's Law and Catching Tax Cheats

2011-06-17T17:08:00.000-05:00

A few years ago, I was looking at a tax blog carnival because it included one of my posts.

One of the other articles was about how, if you get "creative" with your taxes, there is a greater chance that the IRS will flag it because of Benford's Law.

It turns out that Benford's Law is pretty interesting. After reading the article above, I found out more info from the Benford's Law's Wikipedia entry.

The Law deals with the distribution of the first digit in any list of numbers. This could be random numbers, addresses, stock prices, population counts, etc.

Now, your first thought would probably be that the first digit would be evenly distributed between the digits. But, this turns out to be wrong.

Instead, there is about a 30% chance that the first digit would be 1 and the frequency decreases for larger digits - a 9 only has about a 4.6% chance to be a leading digit.

The distribution is logarithmic.

The exact formula is that a digit d (where d is from 1...b-1 and in a base b >=2) occurs as a leading digit with the probability equal to logb((d+1)/d).

So, for our normal base 10 numbering system, this means that the probability of 1 being the leading digit would be logbase10(2/1) = logbase10(2). This would be about .3

I checked this on my unix system using nawk:

[580]-> nawk 'BEGIN {print 10^(.3)}'
1.99526

For 9, it would be logbase10(10/9) = logbase10(1.111), and thus about .046:

[581]-> nawk 'BEGIN {print 10^(.046)}'
1.11173

Simplicity and Focus is the Key to Running A Successful Internet Busness

2011-06-12T02:13:00.000-05:00

A key way to succeed in mathematical and technical disciplines such as designing websites is to apply simplicity and focus.

The web has matured to where it is really hard to successfully create a general site for the masses.

Successful websites today are opportunistic - they spot a specific need and fill it.

One successful site with a clever focus is the website for Blue Sky Scrubs, which make http://www.blueskyscrubs.com/categories/Scrubs/Scrubs-for-Women/.

Because Blue Sky Scrubs keeps its merchandise selection simple and specialized, their website clutter free, well organized, and easy to navigate.

It becomes a snap for visitors to look up whatever types of scrubs clothing they are interested in.

The Boiling Eggs Puzzle

2011-06-12T01:57:00.005-05:00

Can You Generate 24?

2011-06-12T01:57:00.002-05:00

Learn about Scholarships

2011-05-29T01:30:00.001-05:00

Since my readers tend to be interested in education, I like to mention websites that provide service in that area.

I rcently learned about a website that provides free help to find scholarships.

This website is designed in a minimal, simple, and focused style that makes it easy for a visitor to search and locate the right scholarship from him or her.

From the main menu here, a site visitor can easily branch out with one click into sub topics such as engineering grants and grants for physical therapy students.

Summing Consecutive Integers

2011-05-14T07:05:00.001-05:00

A neat fact is that the sum of integers from 1 to N is equal to N * (N+1) / 2.

So, for example, 1+2+3+4+5 is equal to 5*6/2, which is 15.

This fact is really useful if you want to sum huge strings of consecutive numbers, because no matter how many numbers you have, this formula will give you the answer in one calculation.

So, if you actually added up the integers from 1 to 10,000 it would require 10,000 additions. But, you can easily calculate the sum with one calculation: 10000*10001 / 2. which equals 50,005,000.

Thus, a programmer who codes the formula, instead of using brute force addition, would create a program that would run instantaneously, even for adding up millions of integers.

Here is an awk script for summing the integers, which I posted on my unix blog.

Powers and Roots

2011-05-14T06:59:00.003-05:00

Raising a number to a power P means multiplying the number by itself P times.

It is usually denoted with the symbol ^ or **.

For example,

3^0 = 1

3^1 = 3 = 3

3^2 = 3*3 = 9

3^3 = 3 * 3 * 3 = 27

3^4 = 3 * 3 * 3 * 3 = 81

Raising any number to 0 is always defined as 1.

When you use ^2 it is called squaring, and ^3 is calling cubing.

The opposite function is called finding the root. It means taking a number n and a power p, and returning the number that, if raised to power p, will give n. The symbol is hard to show on the computer, so, for a moment, we will just call it rootp().

For example,

root1(3) = 3

root2(9) = 3

root3(27) = 3

root4(81) = 3

Now, just like subtraction is adding a negative number, and dividing is multiplying a fraction, roots can be expressed as raising to a fractional power.

So,

3^(1/1) = 3 because 3^1 = 3

9^(1/2) = 3 because 3^2 = 9

27^(1/3) = 3 because 3^3 = 27

81^(1/4) = 3 because 3^4 = 81

A Hassle-Free Way To Get Important Documents

2011-05-09T14:27:00.000-05:00

In today's complex, suspicious world, we need documentation in order to complete many tasks. For example, you need your child's birth certificate so that you can enroll him or her into school, you may need a marriage certificate for immigration issues, and you may need a death certificate for settling an inheritance or life insurance claim.

It can be complex and time-consuming to get these documents. Frequently, only a certified copy of the document is acceptable - and they require different application processes and fees, depending on the state and/or county.

Since people move around so much, different family members may have been born, married, or died in different areas of the country.

But, internet companies like Vital Chek have sprung up to fill this need. They let you order the documents from one website, and they do all the tracking down and applications for you.

Fw: 9 things that will disappear in our lifetime...

2011-05-03T22:40:00.001-05:00

Subject: Fwd: 9 things that will disappear in our lifetime...

9 things that will disappear in our lifetime...

Whether these changes are good or bad depends in part on how we adapt to them. But, ready or not, here they come.

1. The Post Office.  Get ready to imagine a world without the post office. They are so deeply in financial trouble that there is probably no way to sustain it long term. Email, Fed Ex, and UPS have just about wiped out the minimum revenue needed to keep the post office alive. Most of your mail every day is junk mail and bills.

2. The Check.   Britain is already laying the groundwork to do away with checks by 2018. It costs the financial system billions of dollars a year to process checks. Plastic cards and online transactions will lead to the eventual demise of the check. This plays right into the death of the post office. If you never paid your bills by mail and never received them by mail, the post office would absolutely go out of business.

3. The Newspaper.  The younger generation simply doesn't read the newspaper. They certainly don't subscribe to a daily delivered print edition. That may go the way of the milkman and the laundry man. As for reading the paper online, get ready to pay for it. The rise in mobile Internet devices and e-readers has caused all the newspaper and magazine publishers to form an alliance. They have met with Apple, Amazon, and the major cell phone companies to develop a model for paid subscription services.

4. The Book.  You say you will never give up the physical book that you hold in your hand and turn the literal pages. I said the same thing about downloading music fromiTunes. I wanted my hard copy CD. But I quickly changed my mind when I discovered that I could get albums for half the price without ever leaving home to get the latest music.

The same thing will happen with books. You can browse a bookstore online and even read a preview chapter before you buy. And the price is less than half that of a real book. And think of the convenience! Once you start flicking your fingers on the screen instead of the book, you find that you are lost in the story, can't wait to see what happens next, and you forget that you're holding a gadget instead of a book.

5. The Land Line Telephone.  Unless you have a large family and make a lot of local calls, you don't need it anymore. Most people keep it simply because they've always had it. But you are paying double charges for that extra service. All the cell phone companies will let you call customers using the same cell provider for no charge against your minutes

6. Music.  This is one of the saddest parts of the change story. The music industry is dying a slow death. Not just because of illegal downloading. It's the lack of innovative new music being given a chance to get to the people who would like to hear it. Greed and corruption is the problem. The record labels and the radio conglomerates are simply self-destructing.

Over 40% of the music purchased today is "catalog items," meaning traditional music that the public is familiar with. Older established artists. This is also true on the live concert circuit. To explore this fascinating and disturbing topic further, check out the book, "Appetite for Self-Destruction" by Steve Knopper, and the video documentary, "Before the Music Dies."

7. Television.  Revenues to the networks are down dramatically. Not just because of the economy. People are watching TV and movies streamed from their computers. And they're playing games and doing lots of other things that take up the time that used to be spent watching TV. Prime time shows have degenerated down to lower than the lowest common denominator.

Cable rates are skyrocketing and commercials run about every 4 minutes and 30 seconds. I say good riddance to most of it. It's time for the cable companies to be put out of our misery. Let the people choose what they want to watch online and through Netflix.

8. The "Things" That You Own.  Many of the very possessions that we used to own are still in our lives, but we may not actually own them in the future. They may simply reside in "the cloud." Today your computer has a hard drive and you store your pictures, music, movies, and documents. Your software is on a CD or DVD, and you can always re-install it if need be. But all of that is changing. Apple, Microsoft, and Google are all finishing up their latest "cloud services." That means that when you turn on a computer, the Internet will be built into the operating system.

So, Windows, Google, and the Mac OS will be tied straight into the Internet. If you click an icon, it will open something in the Internet cloud. If you save something, it will be saved to the cloud. And you may pay a monthly subscription fee to the cloud provider. In this virtual world, you can access your music or your books, or your whatever from any laptop or handheld device. That's the good news. But, will you actually own any of this "stuff" or will it all be able to disappear at any moment in a big "Poof?" Will most of the things in our lives be disposable and whimsical? It makes you want to run to the closet and pull out that photo album, grab a book from the shelf, or open up a CD case and pull out the insert.

9. Privacy.  If there ever was a concept that we can look back on nostalgically, it would be privacy. That's gone. It's been gone for a long time anyway. There are cameras on the street, in most of the buildings, and even built into your computer and cell phone.

But you can be sure that 24/7, "They" know who you are and where you are, right down to the GPS coordinates, and the Google Street View. If you buy something, your habit is put into a zillion profiles, and your ads will change to reflect those habits. And "They" will try to get you to buy something else. Again and again.

All we will have that can't be changed are Memories.

My Book "Sudoku Fun: Volume 2" Reached #76 on Amazon.com's Bestseller List for Sudoku Books

2011-05-01T00:30:00.001-05:00

My second Sudoku book, "Sudoku Fun: Volume 2" reached #76 on Amazon.com's Bestseller List for the category "Entertainment->Puzzles & Games->Sudoku".

House Painter's Puzzle - The Simple, Elegant Solution

2011-04-25T23:25:00.000-05:00

(Solution Hidden)

I figured out the simple, elegant solution:

1. The first painter paints at a rate of 1/8 houses per hour.

2. The second painter paints at a rate of 1/12 houses per hour.

3. Therefore, the two painters together will do (1/8 + 1/12) houses per
hour, which simplifies to 5/24 houses per hour.

4. If you know the house per hour rate, then the number of hours to paint
one house is the reciprocral ( 1/house per hour).

5. Thus, it takes the two painters 24/5 hours to do 1 house. This is the
answer of 4 hours, 48 minutes.

House Painter's Puzzle - The Answer

2011-04-19T09:31:00.002-05:00

(Solution Hidden)

Update: Please click here for the simple, elegant solution.

It would take them 288 minutes, which is 4 hours and 48 minutes.

Here is how I solved the problem, though I'm sure there is probably a simple, elegant solution I'm missing:

1. I converted the times to minutes. Thus, painter 1 paints a house in 480 minutes, while painter 2 paints a house in 720 minutes.

2. The faster painter (painter 1) finishes 1/2 the house in 240 minutes. During this time, painter 2 finishes 1/3 of the house. This leaves 1/6 of the house to paint.

3. Painter 1 finishes half of this remaining 1/6 (1/12 of the house) in 40 minutes. In this time, painter 2 paints 1/18 of the house. Thus, we have 1/6 - 1/12 - 1/18 = 1/36 of the house remaining.

4. If we take half of 1/36, we get 1/72 - which doesn't divide evenly into 480 minutes (it gives us 6 and 2/3 minutes). So, I switched to seconds (painter 1 takes 28,800 seconds, painter 2 takes 43,200 seconds). Now, painter 1 takes 400 seconds to paint 1/72 of the house. In that time, painter 2 paints 1/108 of the house. Now we have 1/72 - 1/108 = 1/216 of the house remaining.

5. At this point, I realized that we are doing a series converging on 0. So, I went back to step 4 and used a little thinking. It would take the first painter 6 and 2/3 minutes to paint half the remaining 1/36 (1/72) and painter 2 would have a 1/216 left over. It would take the second painter 10 minutes to paint 1/72 - but that is too long because the first painter would have finished his half. So the final count lies between 6 2/3 minutes and 10 minutes. I tried 8 minutes, and that works.

6. In 8 minutes, the first painter paints 1/60 of the house, and the second painter paints 1/90 of the house. 1/60 + 1/90 = 5/180 = 1/36 - so the house is done!

7. Thus, the painters did the house in 240 + 40 + 8 = 288 minutes, or 4 hours and 48 minutes.

House Painter's Puzzle

2011-04-19T01:57:00.002-05:00

One painter could paint a house in 8 hours, while a second painter could paint a house in 12 hours.

How much time would it take both painters to paint a house?

Please click here for the answer.

Update: Please click here for the simple, elegant answer.

Golfer Puzzle - The Answer

2011-04-16T12:38:00.000-05:00

(Solution Hidden)

The chance of exactly three out of the four golfers getting their own ball is zero.

If three of the golfers choose their own ball, then the only ball remaining for the 4th golfer is his own - so all four golfers will have their own ball.

Golfer Puzzle

2011-04-16T12:35:00.001-05:00

I saw this puzzle in the latest "Ask Marilyn" column in Parade Magazine:

Say that four golfers drive identical balls onto a green, where they land close to one another.

No one knows which ball is whose, so each player randomly chooses a ball.

What are the chances of exactly three of the four golfers selecting their own balls?

Please click here for the answer.

Searching For Online Education Options

2011-04-16T12:18:00.000-05:00

Since many of my readers are interested in education, I thought I would mention about a search portal called FindYourEducation.com that specializes in finding Online Courses for online education.

I like websites that come up with clever, useful niches to specialize in. A search engine for online education is a great one.

Using an education-focused search engine like this one is really efficient because it lets you locate college and degree information quickly.

You can narrow your search to focus on a particular school, or a particular subject, such as online degree programs in finance.

This engine can also refer you to useful education-related sites such as http://www.fafsa.ed.gov/ which is the Free Application For Federal Student Aid.

Interesting Article on Walter Breuning, The World's Oldest Man

2011-04-15T22:57:00.001-05:00

Walter Breuning, the world's oldest man, died Thursday at age 114.

The Associated Press article on his death included his story - based on an interview they did with him last October. It's very interesting reading, because they framed his story in parallel with the history of the U.S.

Some highlights:

0. His mother died at 46, and his father at 50, so he didn't have longevity in the family. His advice for living a long life:

      a) Embrace change.

      b) Eat only 2 meals a day.

      c) Work as long as you can.

     d) Help others.

    e) Accept death.

1. His earliest memory is at 3 - with his grandfather horrifying him by telling stories of killing Southerners during the Civil War.

2. In 1912, his parents split up and he had to work on the railroad at 16. He ended up working there for the next 50 years.

3. His mother died at 46 and his father at 50.

4. In 1919, he bought his first car, and said it spooked the horses that he had to share the street with.

5. He got married in 1922, and bought vacant land for $15. The Depression hit and he was never able to build a house. Eventually he sold the land for $25, making a $10 profit.
He never bought property again and was a lifetime renter.

6. His wife died in 1957 - they had no children, and he never remarried.

Successful Websites Keep It Simple by Focusing On One Need

2011-04-02T18:36:00.002-05:00

I believe that the secret to having a successful internet business is to find one need, then focus on solving it.

For example, there are a lot of people in the United States who want to play poker online. Playing for money is illegal, but there are plenty of legal Sites USA that let you play for fun, and hone your skill.

The problem is that people don't know this list of Online Casinos for USA Players.

I came across several successful sites that simply satisfy this need. They provide lists of the Best US Poker Sites that are legal.

Which Basket Has The 5 Ounce Apples?

2011-04-02T18:09:00.002-05:00

This puzzle is from the Math is Fun website:

The apple farm has 10 baskets of apples. One basket has 5 ounce apples and the other 9 have 4 ounce apples.

You have a measuring scale and an empty basket.

How can you identify the basket of 5 ounce apples by doing only one weighing?

Please click here for the answer.

Cheap Source For Canon Printers

2011-04-01T00:11:00.001-05:00

Many of my readers are students, math educators, programmers, mathematicians, and engineers. A lot of them end up using their printers a lot, and are frequently running low of Canon inkjet cartridges and / or laser toner.

Buying Canon ink refills from retail stores can get very expensive. Fortunately, like many supplies and accessories, shopping the internet can really save you money.

One website that sells Canon printer ink at very reasonable prices is a website called InkGrabber.com.

The Locker Puzzle - The Answer

2011-04-01T00:00:00.001-05:00

(Solution Hidden)

Here is the answer to the locker puzzle:

The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be "changed" an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.

So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.

The Locker Puzzle

2011-03-31T23:58:00.001-05:00

This puzzle is courtesy of pzzls.com:

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

Please click here for the answer.

Simplicity and Focus = Internet Website Success

2011-03-12T02:53:00.000-06:00

A key way to succeed in mathematical and technical disciplines such as designing websites is to apply simplicity and focus.

The web has matured to where it is really hard to successfully create a general site for the masses.

Successful websites today are opportunistic - they spot a specific need and fill it.

One successful site with a clever focus is the website for Blue Sky Scrubs, which specializes in medical scrubs clothing - including lab coats and accessories.

Because Blue Sky Scrubs keeps its merchandise selection simple and specialized, their website clutter free, well organized, and easy to navigate.

It becomes a snap for visitors to look up categories like womens scrubs they are interested in.

Powers and Roots

2011-03-12T02:49:00.001-06:00

Raising a number to a power P means multiplying the number by itself P times.

It is usually denoted with the symbol ^ or **.

For example,

3^0 = 1

3^1 = 3 = 3

3^2 = 3*3 = 9

3^3 = 3 * 3 * 3 = 27

3^4 = 3 * 3 * 3 * 3 = 81

Raising any number to 0 is always defined as 1.

When you use ^2 it is called squaring, and ^3 is calling cubing.

For example,

root1(3) = 3

root2(9) = 3

root3(27) = 3

root4(81) = 3

Now, just like subtraction is adding a negative number, and dividing is multiplying a fraction, roots can be expressed as raising to a fractional power.

So,

3^(1/1) = 3 because 3^1 = 3

9^(1/2) = 3 because 3^2 = 9

27^(1/3) = 3 because 3^3 = 27

81^(1/4) = 3 because 3^4 = 81

Jelly Bean Puzzle

2011-03-12T02:48:00.002-06:00

In a bowl of jelly beans, all but 16 are red, all but 16 are green, all but 16 are blue, and all but 18 are yellow.

How many of each color are in the bowl?

Please click here for the answer.

CarConnection.com

2011-02-20T11:36:00.000-06:00

I like working in areas like unix and the internet because they are meritocracies. Your success is based on your technical skills and execution. You don't have to have the right "connections" or go to the right school.

For example, there is a great alternative to the "famous" car sites - called CarConnection.com. I recently went there to do research on a audi a5. While the other sites simply extended their offline brand to the internet, this site is successful because it is designed specifically for the internet. It has the utility and features that car lovers want in an online site.

The designers made CarConnection a one-stop car portal that allows readers to place classifieds, review cars (such as the cadillac escalade), and discuss topics like insurance, financing, and auto shows.

These features are built around the main function of the site - which is to discuss cars. There are pages and pages of space devoted to both specific models (e.g. audi a8) and car families (e.g. jeep).

Also, the CarConnection is not an example of a pioneering early 1990's site. This website was started after the more famous car sites were created. This site has simply found a place because it provides good information in a good format.

So, while some people think the "golden age" of the internet is over, I think that today is the best time to be involved in computers and the internet. More and more, today's online world is designed around symbiosis - or the idea that millions of niche websites and players are interdependent, and feed off each other's success.

Timing Eggs With Hourglasses Puzzle

2011-02-20T11:32:00.001-06:00

Magic Lily Ponds Puzzle

2011-02-20T11:31:00.001-06:00

Online Tutoring for Math and Chemistry

2011-01-21T23:01:00.000-06:00

An Online Tutoring service can be very convenient because parents won't have to drive their kids back and forth to a classroom. Children also have more confidence because they can learn in the secure environment of their own home. Finally, online tutoring can be much cheaper than hiring a local tutor.

TutorVista is a good example of an online tutoring site. They offer tutoring for elementary school students, as well as college tutor help. They can assist with a wide variety of subjects - for example: Online chemistry help (including Organic Chemistry Tutoring).

Another of their specialties is math tutoring. Math is a fundamental math skill that all children need to learn. TutorVista give help your child learn to Solve math problems. One of the mathematical areas very much in demand is Calculus tutor help.

I especially like the fact that, since the service in online, it costs less than physical tutoring, and is thus more affordable for families on moderate income. It is good if tutors are able to help more kids, because it can make a difference in their future.

Online Logic Puzzles

2011-01-21T22:49:00.001-06:00

I love Puzzler's Paradise because they have lots of interactive logic puzzles that you can solve online.

This way, you do not have to print them out and then solve them with a pen or pencil.

Students at Zoo Puzzle

2011-01-21T22:48:00.001-06:00

Website for Free Samples, Offers, and Downloads

2011-01-18T17:16:00.000-06:00

I recently found a cool site for free stuff called FreeCatcher.com. I like simple, focused sites such as this. It provides a very useful function - a reference to locate all the free marketing offers, searchable by subject. i.e. you can look under the "cell phones" category to find offers for free cell phones.

For a personal example, I love to eat cereal, and enjoy the chance to get free samples of new cereals. I looked on FreeCatcher.com, under "food", and found an offer to get a free sample of the new Cream of Wheat cereal with cinnamon. I just followed the link, typed in my address, and now I should get the cereal sample in the mail. It was quick, easy, and cool!

The greatest part of this site is that it doesn't just list direct advertising offers that require you to give your mail or email information - like samples by mail or email downloads. They also include large companies giving mass market freebies. For example, a large pancake chain offering free pancakes on National Pancake Day.

The fact that the site also lists freebies for National Pancake Day or National Coffee Day make it a more powerful reference tool that lets you track giveaways tied to calendar days.

My experience with FreeCatcher.com is that it is worth it to check it out. It can be fun and profitable to get free stuff!

2 Cars Puzzle

2011-01-18T16:36:00.000-06:00

I'm Included in a Wall Street Journal MarketWatch Article on Bloggers

2011-01-12T14:48:00.002-06:00

http://www.marketwatch.com/story/blogging-all-the-way-to-the-bank-2011-01-12

How Consistency and Focus Are The Keys to Success

2011-01-10T18:57:00.000-06:00

Mistakes in school, math, business, and life are frequently the result of distraction by trying to focus on too many things. We tend to complicate their business over time.

I recently read about a home carpet cleaning services austin business. This business has been around 25 years because they keep things simple and consistent.

They stay focused on their original service (providing healthy home carpet cleaning austin), and gradually expanded into providing naturally complementary tasks such as healthy air duct cleaning services austin and leather cleaning services austin.

By not pursuing opportunities outside their realm of expertise, The Steam Team was able to master their field, build up loyal clientele, and stay up to date on the latest techniques related to carpet and floor cleaning.

Which Word Doesn't Belong?

2011-01-04T12:24:00.000-06:00

This is from the AskMarilyn column in the December 2, 2007 Parade Magazine:

Which of the following words does not belong:

advertisement

automobile

condominium

gymnasium

refrigerator

veterinarian

Please click here for the answer.

The Power of Google Search

2010-12-29T18:45:00.000-06:00

Can You Generate The Number 24?

2010-12-21T13:42:00.000-06:00

Key to Successful Websites - Simplicity and Focus

2010-12-10T13:20:00.000-06:00

A key way to succeed in mathematical and technical disciplines such as designing websites is to apply simplicity and focus.

The web has matured to where it is really hard to successfully create a general site for the masses.

Successful websites today are opportunistic - they spot a specific need and fill it.

One successful site with a clever focus is the website for Blue Sky Scrubs, which specializes in medical scrubs clothing - including white lab coats and accessories.

Because Blue Sky Scrubs keeps its merchandise selection simple and specialized, their website clutter free, well organized, and easy to navigate.

It becomes a snap for visitors to look up whatever types of scrubs sets they are interested in.

9 letter word logic problem

2010-12-07T13:09:00.000-06:00

Candle Length Problem

2010-11-30T00:07:00.000-06:00

This is from an old "Ask Marilyn" column in Parade magazine:

I have two candles, one an inch longer than the other. I light the longer one at 3 pm and the shorter one at 5 pm.

At 9 pm, they're the same length.

The longer candle goes out at 11 pm, and the shorter one goes out at 10:30 pm.

How long were they at the start?

Please click here for the answer.

A little more than whale watching

2010-11-15T18:28:00.000-06:00

Guest post written by Bret Sommers

I've never really been interested much in marine biology, so when I saw that one of my favorite authors wrote about people who do research on whales I thought it was pretty weird. Especially because he writes about a whole lot of crazy and supernatural stuff. His name's Christopher Moore and even though he writes about supernatural stuff, his stuff is really hilarious.

I went online to see if my local library had it by looking through its card catalogue. When I was doing that I ran across this site www.cleartvbundle.com and decided to switch over my internet service to it after going through all of it.

Well, my local library didn't have Christopher Moore Fluke, which didn't surpirse me all that much because it seems like my library never has hardly any good books. Which makes me think that maybe I should just start requesting for better books. I think that other people would appreciate that so that more people could read books that are by some funny authors and not on high schoolers reading lists.