Combine 1,3,3,7 to get 10

Question

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

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 '23 at 08:36
Is "concatenating initial digits to create a word" allowed? Because LEET speak is 10 out of 10. — candied_orange, Jun 23 '23 at 04:39

justhalf · Answer 1 · 2023-06-22T10:02:52.487

48

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:

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

edited Jun 22 '23 at 10:02

answered Jun 21 '23 at 19:55

justhalf

1

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! – Janus Bahs Jacquet Jun 23 '23 at 14:39
3

@JanusBahsJacquet you should still be proud if you find it yourself! :D – justhalf Jun 24 '23 at 03:42

score 2 · Answer 2 · answered Jun 21 '23 at 16:59

2

If concatenation is allowed, then one solution is

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

answered Jun 21 '23 at 16:59

Prim3numbah

2

If indices/powers were permitted as well as concatenation, there's another possible solution in this question on the site. – Stiv Jun 21 '23 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. – Prim3numbah Jun 21 '23 at 18:37
2

Unfortunately, concatenations do not seem to be allowed. – Karl Karlsen Jun 21 '23 at 19:24

score 0 · Answer 3 · edited Jun 21 '23 at 20:18

0

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 $

edited Jun 21 '23 at 20:18

fljx

answered Jun 21 '23 at 18:57

theozh

6

Yes, I had that one, too :) Unfortunately not allowed. Also 1+3+3+7 =10 in tetradecimal would be nice. – Karl Karlsen Jun 21 '23 at 19:19
I guess $7-3-1=10_3$ is also no go? – Oscar Lanzi Jan 21 '24 at 20:35

3 Answers3