# 2023 From Single Digits

Using only the digits, 1, 2, 3, 4, 5, 6, 7, 8, and 9, in that order, how can you make the number 2023 using the +, -, ✕ and ÷ operations? (You can use as many parentheses as you want)

• There are two solutions, one has already been found. May 1, 2023 at 22:41
• Clue: $2023=7^2\times17$ May 2, 2023 at 4:08
• I think you mean $2023=7*17^2$. May 2, 2023 at 4:20
• yes, right. thank you May 3, 2023 at 12:14

I don't think this one has been said yet:

$$(1 - 2 - 3*4 + 5*6)*7*(8 + 9)$$

No division needed here either!

• Yes, very similar to the one by isaacg. May 5, 2023 at 15:03
• @RonnieChen agreed, yet somehow distinct! May 5, 2023 at 16:15

Using the fact that $$7*17*17=2023$$,

$$(1-2+3+4+5+6)*7*(8+9)$$

No division needed!

Here is the answer with only using $$+$$, $$\times$$, and $$\div$$ without any parentheses and $$-$$;

$$1+2*3+4*567*8/9$$

• Sorry, you cannot combine digits to form a multi-digit number. May 1, 2023 at 22:39
• @RonnieChen in the question, you do not say you can use parentheses either :)
– Oray
May 2, 2023 at 7:15
• Actually, this is the most accurate answer given the question as it is written: digits are "pieces" of a number and parentheses aren't in the allowed symbol list. Great job! May 2, 2023 at 10:05

Here's a solution using all the operations and the digits in the same order.

$$((-(-1)/2)*3*4)+5+6)*(7*(8+9))$$

Some proofs

Solve path

I looked for factors of 2023 and found 17 and 119. Looked for factors of 119 and found 7 amd 17. Tada, I can use 7,8,9 to get 119. Now, 17 is a prime number. No factors. So, a bit of trial and errors and we can easily use digits 1,2,3,4,5,6 to get 17. Idea was to use bigger digits 5,6 with additions/substractions and smaller ones for other operations.

• That is correct, there is another solution May 1, 2023 at 22:40

There are a number of solutions, but the first one I came across was:

(1 + 2 + 3) * 4 * 5 + 6 - 7 * (8 + 9)

• this is equal to 7
– Oray
May 1, 2023 at 21:08
• Looks like ((1 + 2 + 3) * 4 * 5 + 6 - 7) * (8 + 9) was actually meant. Or (1 * 2 * 3 * 4 * 5 + 6 - 7) * (8 + 9), for fewer parentheses. May 2, 2023 at 10:49
• Evidence: dc <<<'1 2 3 4 5 **** 6+ 7- 8 9+*p' May 2, 2023 at 10:53