My Maths teacher taught us how to play a game called 31 on Friday. Not once did my Maths teacher lose. I want to know why.
I'll explain the game...
31 is a game between two people.
Let's say you've got a grid of numbers - 6 rows, 4 columns. Each column contains the numbers 1-6, such that the first row will contain only 1's, the second will contain only 2's and so on.
Player one begins by choosing an entry from the grid, crossing it off and recording the number chosen. Player two then chooses another entry from the grid (could be the same number), crosses it off and adds this to the number previously recorded. Once an entry has been crossed off, it cannot be reused. The objective is to make the total reach 31 on your turn.
I've established that if you make the total reach 24 on your turn, the next turn a number would have to be chosen which would not allow the total to exceed 30, and hence you would win on your next turn, providing that the entry required to reach 31 had not been crossed off. Furthermore, if you make the total reach 17 on your turn, the next turn a number would have to be chosen which would not allow the total to exceed 23, and hence you would reach 24 on your next turn, providing that the entry required to reach 24 had not been crossed off. Further "magic numbers" are hence 10 and 3.
Using this "magic number" logic, I decided to attempt to beat my Maths teacher. He still beat me - I reached 24 no problem, but ran out of entries in a row (sorry - cannot remember which, think it was row 3), and so, he was crowned the winner to yet another student.
I'm really struggling to devise a fail-proof method. Can you please assist me?