# 10 9 8 7 6 5 4 3 2 1 = 2017

Add the four basic operators $\times\div+\,\;-$ and optionally brackets to:

$10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$

To get the total $2017$.

Rules:

• Look for the simplest solution - i.e. the least amount of characters (ignoring spaces). Please include your character count in your answer.
• Keep the order; do not add or combine numbers.
• Use all four operators at least once.

Credit for initial concept: Alex Bellos

Previous year: here.

• Is implicit multiplication allowed? – Beastly Gerbil Jan 1 '17 at 12:11
• For best solution you can mix up the numbers like 109X87+6543-21 – Black Mamba Jan 1 '17 at 13:27
• As of 2017 Code Golf is invading puzzling. – Zxyrra Jan 1 '17 at 16:05
• Just being curious about it: is there a known algorithm to solve it? (given inputs: list of possible numbers, desired result). I'm thinking about dynamic programing. Also don't know how I could call this problem to look for litterature. – pltrdy Jan 2 '17 at 11:57
• @pltrdy Have you read this post? – xzczd Jan 5 '17 at 14:58

This one is 20 characters:

$10×9×8×7 \div 6 \div 5×4×3 + 2 - 1$

• @Paparazzi thanks - I think I left my counting skills in 2016. – Glorfindel Jan 1 '17 at 12:42
• Will work for the next two years as well (changing the final - to a x or +) – Tom Carpenter Jan 1 '17 at 15:26
• @TomCarpenter And it would also work for 2013-2015 by flipping the sign for 2 and manipulating the operator for 1 accordingly. This should also be the shortest answer, considering it has no brackets. – Reti43 Jan 1 '17 at 23:54
• I wrote a script to try all combinations without parenthesis, this is the only one it finds. – C5H8NNaO4 Jan 2 '17 at 2:35
• @TomCarpenter no it would not: a - sign would be missing. – Cœur Jan 2 '17 at 11:36

One can even find $2017$ by using only 5 numbers given in the question without changing the order as below:

$9×8×7×4+1=2017$

Here are the actual answers for the question:

1. $(10+9×8×7-6-5)×4+3+2×1=2017$ - 22 Chars

2. $(10×9×8×7)\div((6×5)\div(4×3))+2-1=2017$ - 28 Chars

3. $10×9×8×7×6\div5\div(4-3+2)+1=2017$ - 22 Chars

4. $(10+9×8×7-6-5)×4+3+2\div1=2017$ - 22 Chars

5. $10×9×8×7\div(6+5+4)×3×2+1=2017$ - 22 Chars

6. $10-9+8×7×6×(5-4)×3×2\div1=2017$ - 22 Chars

7. $(10-9+8)×7×(6-5+(4-3)×2)+1=2017$ - 26 Chars

8. $(10+9)×8×(7+6)+5+4×3×(2+1)=2017$ - 26 Chars

• You can simplify some of those, considering a ÷ (b ÷ c) = a ÷ b × c and a ÷ (b × c) = a ÷ b ÷ c – Daerdemandt Jan 1 '17 at 20:35
• #3 has mismatching brackets – vrwim Jan 2 '17 at 0:49
• Can you include the number of characters for each? – IAmInPLS Jan 2 '17 at 11:17
• @IAmInPLS fixed all errors... – Oray Jan 2 '17 at 11:45

22 characters:

$10×9×8×7×6÷5÷(4−3+2)+1$

$10×9×8×7×6÷(5+4×3−2)+1$