If you have 15 straws what number of straws would you need to pick to win every time if you and the other person are allowed to either pick one or two straws at a time going back and forth and the person to pick the last straw loses?
To win you must be able to leave him with 1 straw so he will have no choice but to pick it up last.
That is only possible if before that he left you with 2 or 3 straws.
That is only possible if before that you left him with 4 straws.
That is only possible if before that he left you with 5 or 6 straws.
That is only possible if before that you left him with 7 straws.
That is only possible if before that he left you with 8 or 9 straws.
That is only possible if before that you left him with 10 straws.
That is only possible if before that he left you with 11 or 12 straws.
That is only possible if before that you left him with 13 straws.
So if you get to start first, then you can always win if you begin by
picking 2 to begin with, leaving him with 13, then with 10, then with 7,
then with 4, and finally with 1.
If he starts first, you can still win if he ever leaves you with any number
other than 13, 10, 7, 4, or 1.
Edwin
