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I tried lots of combinations but could not find a solution. Each number has to be used exactly once, the allowed mathematical operators are

  • Addition: +
  • Subtraction: -
  • Negation: (unary prefix) -
  • Multiplication: *
  • Division: /
  • Grouping with parentheses: ( )

All other operations (including the often implicitly accepted "concatenating initial digits to create a multi-digit number") are disallowed.

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    $\begingroup$ With some low-effort answers already coming in, I clarified the intent of the operator list you gave, hope this is what you meant. Don't want anyone saying "the parens can be used as the choose operator, so ${7 - 3 + 1 \choose 3} = 10$", now do we :-) $\endgroup$
    – Bass
    Jun 22 at 8:36
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    $\begingroup$ @Bass that was used in a puzzle before indeed, haha $\endgroup$
    – justhalf
    Jun 22 at 9:55
  • $\begingroup$ Is raising to a power allowed (see my answer)? $\endgroup$
    – Vilx-
    Jun 22 at 10:13
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    $\begingroup$ Is "concatenating initial digits to create a word" allowed? Because LEET speak is 10 out of 10. $\endgroup$
    – candied_orange
    Jun 23 at 4:39
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    $\begingroup$ Maybe so, but "10 out of 10" or 10 / 10 is 1 :-) $\endgroup$
    – cmbuckley
    Jun 26 at 9:52

3 Answers 3

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As quite standard in this kind of hard number puzzle, we can:

use addition on a fraction: $$\left(\frac{7}{3}+1\right)\times 3 = 10$$

Another example of this form being the only solution is:

Use 1, 2, 3, 8 to make 28

with the unique (up to commutation) solution being:

$$\left(\frac{1}{2}+3\right)\times 8 = 28$$

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    $\begingroup$ Dammit, I just spent a good ten minutes moving numbers around in my head and felt so proud to have finally got it – only to realise it was right there in the highest-voted answer! $\endgroup$
    – Janus Bahs Jacquet
    Jun 23 at 14:39
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    $\begingroup$ @JanusBahsJacquet you should still be proud if you find it yourself! :D $\endgroup$
    – justhalf
    Jun 24 at 3:42
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If concatenation is allowed, then one solution is

$31 - 7*3 = 31 - 21 = 10$

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    $\begingroup$ If indices/powers were permitted as well as concatenation, there's another possible solution in this question on the site. $\endgroup$
    – Stiv
    Jun 21 at 18:16
  • $\begingroup$ That was actually my initial answer, but since 3³ is 3^3 and uses a "^", which isn't allowed, I chose to go for the answer above. $\endgroup$
    – Prim3numbah
    Jun 21 at 18:37
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    $\begingroup$ Unfortunately, concatenations do not seem to be allowed. $\endgroup$
    – Karl Karlsen
    Jun 21 at 19:24
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The following is trivial, but (at least up to now) not explicitly forbidden by OP's definition:

in octal system: $ 1 + 3 - 3 + 7 = 10 $

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    $\begingroup$ Yes, I had that one, too :) Unfortunately not allowed. Also 1+3+3+7 =10 in tetradecimal would be nice. $\endgroup$
    – Karl Karlsen
    Jun 21 at 19:19

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