How will Y lose the game ?X and Y are playing a game. There are eleven coins on the table and each player must pick up at least one coin but not more than five in a turn. The person picking up the last coin loses. X starts. How many should X pick up to start to ensure a win no matter what strategy Y employs
X picks 4.
Y picks coins.
X removes coins.
There is now 1 coin on the table because we removed .Generalization.There are coins on the table and one player can pick as many as M coins at once.Case 1:
M >= K. This is trivial. Player 1 picks coins, leaving 1 coin and wins.
Case 2.1:
and
player 1 picks coins in such a way that
player 2 picks coins ().
Player 1 picks coins leaving again the number of coins on the table
Repeat this process until and player 1 wins.
Case 2.2
and
Player 2 can follow the same strategy as player 1 followed in case 2.1 and win.
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