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Puzzle 6 | (Poison and Rat)
There are 1000 cheese pieces. One of the pieces contains poisoned cheese. A rat dies after one hour of eating the poisoned cheese. How many minimum rats are needed to figure out which piece contains poison in hour.
Solution :
We need to figure out in hour. We need 10 rats to figure out the poisoned cheese. The result is based on binary number system. We get 10 using $[\log_{2}{1000}]$.
The idea is to number cheese pieces from 1 to 1000 and write their corresponding binary numbers on the pieces. Each rat is assigned a position in the binary numbers written on pieces. Let us take an example. Rat 1 represents first bit in every piece, rat 2 represents second bit and so on. If rat numbers 5, 7 and 9 die, then piece number 42 (Binary 0000101010) is poisoned.