Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also integers.
How much does each pumpkin weigh?
Since 4*(sum of the weights) = 216, then the sum is 54.
Now, we notice that there are 6 even numbers in the list, and 4 odd ones. This could only happen if there was only 1 odd weight, or only 1 even weight. One odd weight can't happen, since the sum of the weights is even. This we conclude that the even weight is inside the odd sums 19, 21, 23, and 27. And subtracting the even weight from these would give you the other four weights.
But it happens that 19+21+23+27 = 3(even weight)+(sum of the weights). So the even weight is 12. The rest of the numbers follow.

Posted by Jake
on 20080406 20:33:04 