--description--

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,

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.

--hints--

arithmeticExpressions() should return a number.

assert(typeof arithmeticExpressions() === 'number');

arithmeticExpressions() should return 1258.

assert.strictEqual(arithmeticExpressions(), 1258);

--seed--

--seed-contents--

function arithmeticExpressions() {

  return true;
}

arithmeticExpressions();

--solutions--

// solution required