Lesson Three: Thinking outside the box

Last week I met with Mr. Markey, Rachel Gray, and Thomas Esch to discuss some problem solving. After outlining the four steps of problem solving, Mr. Markey introduced a neat way of looking at a basic problem.

Here's the problem. As you solve it, think as many different ways of solving it as possible.

Problem One: There are 64 teams which take part in March Madness each year. How many games are played before a winner is crowned NCAA champion?








***Think about different ways of solving it before reading the answer below***














Mr. Markey presented this alternate way of solving the problem. Instead of trying to calculate each game played using powers of two or something like that, think about the format of the tournament. Each team which does not win the entire tournament loses exactly one game before being kicked out of the tournament. Given that only one team goes undefeated throughout the entire tournament. This implies that 63 of the 64 teams lose exactly one game, meaning that exactly 63 games were played.

While this problems isn't "SUPER HARD", I thought it was a great example of the most elegant solution arising from looking at the problem in a different light than what I initially thought of for solvivg this problem.

Hope you enjoyed it as much as I did.