The King's Party

Think about binary strings.

Since every prisoner can end up dead or alive, there are 2^10 = 1024 possible outcomes. Since 1024 > 1000, it's actually possible to use an approach using binary strings.

• The king assigns each servant a number from 1 to 10.
• The king assigns each bottle a number from 0 to 999.

When he labels them, he writes the number on the bottle in binary with ten digits, like this:

• 0: 000000000
• 1: 000000001
• 2: 000000010
• 3: 000000011
• 4: 000000100
• ...
• 999: 1111100111.

The strategy is simple: the king assigned the prissoners a number from 1 to 10, indicating the position of the number in the binary string. If the string has a number one on the - let's say - fifth- and sixth position, then the prisoners with number five and six have to drink the wine. After less than four weeks, suppose only prisoners number five and six die. This means the binary representation of poisoned wine has a '1' at position five and six, and the rest are all zeros.

Convert this binary number to a decimal and that gives you the number of the poisoned wine.

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