# Combine 1,3,3,7 to get 10

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

• 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.

• 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 :-)
– Bass
Jun 22 at 8:36
• @Bass that was used in a puzzle before indeed, haha Jun 22 at 9:55
• Is raising to a power allowed (see my answer)? Jun 22 at 10:13
• Is "concatenating initial digits to create a word" allowed? Because LEET speak is 10 out of 10. Jun 23 at 4:39
• Maybe so, but "10 out of 10" or 10 / 10 is 1 :-) Jun 26 at 9:52

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:

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

• 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! Jun 23 at 14:39
• @JanusBahsJacquet you should still be proud if you find it yourself! :D Jun 24 at 3:42

If concatenation is allowed, then one solution is

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

• If indices/powers were permitted as well as concatenation, there's another possible solution in this question on the site.
– Stiv
Jun 21 at 18:16
• 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. Jun 21 at 18:37
• Unfortunately, concatenations do not seem to be allowed. Jun 21 at 19:24

The following is trivial, but (at least up to now) not explicitly forbidden by OP's definition:

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

• Yes, I had that one, too :) Unfortunately not allowed. Also 1+3+3+7 =10 in tetradecimal would be nice. Jun 21 at 19:19