# It's broken, but better

**Number Theory**Level 4

A merchant had a forty-pound 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 pounds and that the four pieces could be used to weigh every integral weight between 1 and 40 pounds.

Let the weights of the pieces be \(a,b,c,d\) such that \(a\leq b\leq c \leq d\), what is the value of \(\overline{abcd}\)?

If \(a,b,c,d\) were \(1,4,23,56\), input your answer as \(142356\).