Here I start a new section called problem of the week. Solution of this question will be posted in the coming week. Till then have fun.

Alphonse and Beryl are back! They are playing a two person game with the following

rules:

• Initially there is a pile of N stones, with N >= 2.

• The players alternate turns, with Alphonse going first. On his first

turn, Alphonse must remove at least 1 and at most N −1 stones from

the pile.

• If a player removes k stones on their turn, then the other player must

remove at least 1 and at most 2k − 1 stones on their next turn.

• The player who removes the last stone wins the game.

(a) Determine who should win the game when N = 7, and explain the winning

strategy.[Easy]

(b) Determine who should win the game when N = 8, and explain the winning

strategy.[Medium]

(c) Determine all values of N for which Beryl has a winning strategy. Explain this

strategy.Where N<=100[Difficult]

## Monday, January 11, 2010

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