data/problems/93.yml
---
:id: 93
:name: Arithmetic expressions
:url: https://projecteuler.net/problem=93
:content: "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.\n\nFor example,\n\n8
= (4 \\* (1 + 3)) / 2 \n14 = 4 \\* (3 + 1 / 2) \n19 = 4 \\* (2 + 3) − 1 \n36
= 3 \\* 4 \\* (2 + 1)\n\nNote that concatenations of the digits, like 12 + 34, are
not allowed.\n\nUsing 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.\n\nFind
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_.\n\n"