# Form a number using some numbers and mathematical operations

Using 2,3,4,5,6,7 and basic mathematical operations form the number 1088.

Every digit must be used exactly once (neither zero nor greater than one times). Concatenation of digits (such as 53) is not allowed. Each operator can be used multiple times or not at all in any combination. This removes duplicates and creates it as having a unique solution.

Note:

Allowed Operations: $+,-,/,*, {}^{\displaystyle\large\hat{}} ,!,\sqrt{}$

• Must we use all provided numbers or can we use only a subset of them? Do you allow repeats? Can we combine numbers to form multi-digit numbers (e.g. 23, 57 etc)? Also, is ^ exponentiation or XOR? – user12205 May 11 '15 at 12:41
• @ace Every digit exactly once. – RE60K May 11 '15 at 13:05
• ADG, you should explicitly state (edit it in) that parentheses are allowed if they are allowed. – Olive Stemforn Jun 20 '15 at 16:56

Update: This 4-operator answer is now disallowed by OP after rule change. The 6-operator one still works though.

An answer that uses 4 operators only (assuming concatenation to form multi-digit numbers is allowed):

$$523 \times \sqrt4 + 6 \times 7 = 1088$$

Assuming we can use parentheses and they don't count as operators, then we have 6 operators with

$$7^3 + 6! + 5 ^ {(4-2)} = 1088$$

If we can't use parentheses, then

$$7\;3\;{}^\wedge\;6\;!\;+\;5\;4\;2\;-\;{}^\wedge\;+$$

which is the same thing in reverse Polish notation.

The above assumes that the ^ operator is for exponentiation, not XOR.

• You can remove the parentheses in any case since $5^{4-2}$ is unambiguous. – Lawrence May 12 '15 at 15:06
• @Lawrence I know, but the OP mentioned the ^ operator, not exponentiation. If we are to use the ^ operator, we would need to write 5^(4-2) with parentheses needed. I'm not sure how the OP wants his answers. – user12205 May 12 '15 at 15:13
• I see - good call then :) . – Lawrence May 12 '15 at 15:14
• From OP: "No concatenation" Your solutions using 523 and 73/542 are invalid. – Engineer Toast May 12 '15 at 15:38
• @EngineerToast The OP stated that rule after my submission. (I asked him in the comments but he did not reply.) Also, the last entry is the same as the second but written in reverse Polish notation. – user12205 May 12 '15 at 15:43

7!/5 + 6!/(2+3+4)

Here is another possible solution:

$(5!/4 \ + \ 3)^2 \ - \ 7 \ + \ 6 \ = \ 1088$

One other possible answer: $$6! \times \frac{3}{2} + 5 + 7 - 4 = 1088$$

$1088=2^{(2*5)}+64$
$1088=2^{(3+7)}+64$