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Alice and Bob play the following coins-on-a-stack game. 20
coins are stacked one above the other. One of them is a
special (gold) coin and the rest are ordinary coins. The
goal is to bring the gold coin to the top by repeatedly
moving the topmost coin to another position in the stack.
Alice starts and the players take turns. A turn consists of
moving the coin on the top to a position i below the top
coin (0 = i = 20). We will call this an i-move (thus a 0-
move implies doing nothing). The proviso is that an i-move
cannot be repeated; for example once a player makes a 2-
move, on subsequent turns neither player can make a 2-move.
If the gold coin happens to be on top when it's a player's
turn then the player wins the game. Initially, the gold
coinis the third coin from the top
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Answer Posted / abhishek
if Alice takes 0: then 2 coins left over gold, now B takes
>=2 then 1 coin left above gold..Alice cannot take 0..any
other will make the gold at top. so not 0
If alice takes 1 at first then 2 coins left. . now B can
take 0 or anything >=2.
If B takes 0,then no change..now A takes 2 leaving 1 coin
above gold..what ever b takes A wins.
If B takes 2 then one coin left above gold then A takes
zero.. now what ever B takes A wins
So 1 first
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