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There are two candles with different thickness, but are of equal length. The thicker one lasts of six hours and the thinner candle last for 2 hours less than the thicker one. Suresh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. For how long did Suresh light the two candles.
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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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