whichcoin

whichcoin - Which Coin is False - - - - Consider the...

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Sheet1 Page 1 Which Coin is False ----- ---- -- ----- Consider the following problem. You are given N coins, exactly 1 of which is false, in that its weight differs from the others, though you do not know whether the false coin is lighter or heavier than it should be. You are also given 1 additional coin known to be true and a scale. You are asked to make a series of weighings of equal numbers of the coins and at the end tell which coin is false. You are asked to minimize the number of weighings required. Professor Toowit Toowoo (TT to his friends) has come up with the following strategy for solving this problem. There are two cases: first, where you do not know whether the false coin is lighter than or heavier than a true coin, and second where you do know. If you do know whether the false coin is lighter than or heavier than a true coin, divide the N coins into three almost equal groups, and weigh two of these that have equal numbers of coins against each other. The result will tell you which of the three groups the false coin is in. If on the other hand you do NOT know whether the false

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This note was uploaded on 04/29/2011 for the course IT 201 taught by Professor K.v.arya during the Spring '11 term at IIT Kanpur.

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whichcoin - Which Coin is False - - - - Consider the...

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