BizzClick

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?

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.

Introduction to Roots and Powers

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

      

Scholarship Info Site

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)

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

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

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

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

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

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

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.