# Problem 93: Arithmetic expressions

![graphic](img093.gif)

By using each of the digits from the set, {1, 2, 3, 4}, exactly once,
and making use of the four arithmetic operations (+, −, \*, /) and
brackets/parentheses, it is possible to form different positive integer
targets. For example, 8 = (4 \* (1 + 3)) / 2 14 = 4 \* (3 + 1 / 2) 19 =
4 \* (2 + 3) − 1 36 = 3 \* 4 \* (2 + 1) Note that concatenations of the
digits, like 12 + 34, are not allowed. Using the set, {1, 2, 3, 4}, it
is possible to obtain thirty-one different target numbers of which 36 is
the maximum, and each of the numbers 1 to 28 can be obtained before
encountering the first non-expressible number. Find the set of four
distinct digits, a < b < c < d, for which the longest set of
consecutive positive integers, 1 to n, can be obtained, giving your
answer as a string: abcd.