# If ninety camels are to be tied up to nine different poles, suggest a way to tie them such that the number of camels in each pole is odd.

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### 1 Answer

It would be impossible to use all nine poles. To see this, note that an odd number plus an odd number is always even. I'll shorten this to

odd+odd=even.

Also, even+odd=odd, so we can say that

odd+odd+odd=(odd+odd)+odd=even+odd=odd.

The pattern continues. *Adding and even number of odd numbers always results in an even number. Adding an odd number of odd numbers always results in an odd number.*

So if each of the nine poles had an odd number of camels, there would have to be an odd number of camels total, but 90 is even, so it is impossible.

If you don't have to use every pole, then there is the easy solution of tying 89 to one pole and 1 to another pole. A more interesting problem would be to find the greatest number of poles that can be used. Can you tie them all to eight poles and have an odd number at each? I haven't tried it yet.

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