A merchant had a 40 kg measuring weight that broke into four
pieces as the result of a fall. When the pieces were subsequently
weighed, it was found that the weight of each piece was a whole
number of kilograms and that the four pieces could be used to
weigh every integral weight between 1 and 40 kg. What were the
weight of the pieces.
Note:Weights may be places in either pan of the balance.