Category: College Mathematics

Dominoes and Mathematical Induction

College Mathematics, Number Theory

Dominoes are Falling Down

If you queued ten thousand dominoes on a very long table and you want to let them all fall just by letting the first domino fall, then how would you queue it?

The best idea probably is to queue them such that:

  1. When the first domino falls, it will hit the second domino.
  2. Make sure that each domino will hit the domino next to it and that each hit domino will fall.
  3. If conditions (1) and (2) are satisfied, then all the dominoes will fall.

The domino effect

In fact, no matter how many dominoes we put on the table, as long as conditions (1) and (2) are satisfied we are sure that all the dominoes will fall. » Read more

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Using Mathematics to Win the Lottery

High School Mathematics, Math in Real Life, Probability and Statistics

Lottery Basics

Many of you are probably familiar how lottery works.  A lottery is a game where a smaller group of numbers is chosen from a larger group. If you bet on the right combination, you win the jackpot prize, which is usually staggering.

lottery1

Although there is a common concept about lottery, there are variations in different places or countries.  In this post, I will use ours as an example. In the Philippines, as of this writing, we have three types of lottery: 6/42, 6/45 and 6/49. Yes, you guessed it right, 6/42 means 6 numbers are randomly chosen from a set of numbers from 1 through 42. We use the 6/42 lottery in the following discussion. » Read more

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Young Gauss and the sum of the first n positive integers

College Mathematics, High School Mathematics, Number Theory

Carl Friedrich Gauss was one of the most prolific mathematicians of all time. In fact,  he was considered by many as the “Prince of Mathematicians” because of his numerous contributions in different fields of mathematics.

Gauss displayed his genius at an early age. According to anecdotes, when he was in primary school, he was punished by his teacher due to misbehavior.  He was told to add the numbers from 1 to 100. He was able to compute its sum, which is 5050, in a matter of seconds.

Old Gauss

Now, how on earth did he do it? » Read more

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