ou have only four weights and a balance scale. If your task is to weigh ANY load from 1 to 40 kg (integers only) then how much should each of your 4 weights weigh?

Answer 1

This a tough question. I found the answer with an online search,
at http://www.funtrivia.com/askft/Question26870.html ,
but probably would not have been able to figure it out myself for hours.

You do it with four weights (1, 3, 9 and 27) by putting weights on both sides of the scale. For example, to weigh something that is 25 pounds, you put 27 and 1 on one side, 3 on the other side, and the item you are weighing on the same side as the 3.

For an 11 lb weight, put 9+3 lb on one side and 1 lb with the unknown on the other side. For 19, put 27+1 on one side and unknown + 9 on the other side. There is always a way.

Note that the total of all weights is 40, so can measure a 40 lb weight by putting them all on one side.