data/problems/259.yml
---
:id: 259
:name: Reachable Numbers
:url: https://projecteuler.net/problem=259
:content: |+
A positive integer will be called _reachable_ if it can result from an arithmetic expression obeying the following rules:
- Uses the digits 1 through 9, in that order and exactly once each.
- Any successive digits can be concatenated (for example, using the digits 2, 3 and 4 we obtain the number 234).
- Only the four usual binary arithmetic operations (addition, subtraction, multiplication and division) are allowed.
- Each operation can be used any number of times, or not at all.
- <dfn title="A minus sign applied to a single operand (as opposed to a subtraction operator between two operands)">Unary minus</dfn> is not allowed.
- Any number of (possibly nested) parentheses may be used to define the order of operations.
For example, 42 is reachable, since (1/23) \* ((4\*5)-6) \* (78-9) = 42.
What is the sum of all positive reachable integers?