# It's broken, but better

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 $$142356$$.

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