A train blows a siren one hour after starting from the station. After that it travels at 3/5th of its speed it reaches the next station 2 hours behind schedule. If it had a problem 50 miles farther from the previous case,it would have reached 40 minutes sooner. Find the distance between the two stations .
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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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