Past Problems of the Month

We, the Mathematical Society of TAMIU, believe that everyone, math lovers and haters, has the innate ability to think mathematically, and that everyone should be given a chance to have fun by flexing their math brains. We have decided to sponsor the “Problem of the Month,” and reward you with great prizes for solving our problems; prizes such as Buck's tickets and fine dinners at various restaurants. Clicking the link below will give you further information and how to enter. Below is the problem of the month.

Click Here for Complete Rules and Instructions

 

 

Problem of the Month for December 2002

 

Problems of the Month, December 2003

Elementary Problem — Addition Games
This month, we have two games involving addition. Both games are played
between two players. As in chess, the players take turn to make their moves.
Game 1. This game starts with the number 0. In one turn, each player
adds a number from 1 through 7 to the current number. The player who
first reaches the number 25 wins.

For example, between two players A and B,
A adds 5 to 0 and says, 5.
B adds 6 to 5 and says, 11.
A adds 1 to 11 and says, 12.
B adds 3 to 12 and says, 15.
A adds 4 to 15 and says 19.
B adds 6 to 19 and says 25, and B wins!

What is the best strategy to play this game?

Game 2.

This game begins with the number 2. In one turn, each player
adds to the current number any natural number smaller than it: for
example, when the current number is 18, you can add to it any number from 1 through 17. The player who first reaches the number 100 wins.
What is the best strategy to play this game?

Play these games with friends and see if you can come up with a strategy.

You may change the goal numbers (25 or 100) so that the game would last longer or shorter. When you think you found a winning strategy for either of the games, send it in.
Have Fun!

Advanced Problem — A Subtraction Game

The Game: This game starts with the number 1000. Two players take
turn to subtract any power of 2 (including the 0th power, 1) from the
current number. The player who first reaches the number 0 is the winner.
Problem: Find the best strategy for this game.
Hint: You might change the initial number 1000 to different numbers and
see if you can discover a pattern. The strategy is rather unexpected, but
turns out to be pretty simple.