Name: Bev
Who is asking: Other
Level of the question: All
Question: 5 men took turns weighing themselves on a scale. However, they weighed each other two at a time, ten times total, so that every possible combination of two men was weighed. The scale had the following read out for the pairs, 236,244,228,250,258,230,246,238,242,and 252 pounds. How heavy was the heaviest man?
This question came from my granddaughter, any help would be
appreciated.

Bev,
 Add up all these weights, and you get four times the total weight of the five men (because each man went four times on the scale). So if you divide this number by four you get the total weight of all five men.
 The largest number on the list has to be the combined weight of the two heaviest men, and the smallest number on the list has to be the combined weight of the two lightest men. When you subtract these two numbers from the total weight, you get the weight of the middle man.
 The second largest number on the list has to be the combined weight of the heaviest and the middle man, so you only need to subtract from it the weight of the middle man to get the weight of the heaviest.
Claude
