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

Question

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.}

For best solution you can mix up the numbers like 109X87+6543-21 — Black Mamba, Jan 01 '17 at 13:27
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 02 '17 at 11:57
@xzczd ty. It actually looks not straightforward :p Thats what i asked ty — pltrdy, Jan 05 '17 at 15:10

Glorfindel · Accepted Answer · 2017-01-01T12:41:59.917

22

This one is 20 characters:

$10×9×8×7 \div 6 \div 5×4×3 + 2 - 1$

edited Jan 01 '17 at 12:41

answered Jan 01 '17 at 12:21

Glorfindel

28,033
9
96
142

6

@Paparazzi thanks - I think I left my counting skills in 2016. – Glorfindel Jan 01 '17 at 12:42
8

Will work for the next two years as well (changing the final - to a x or +) – Tom Carpenter Jan 01 '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 01 '17 at 23:54
I wrote a script to try all combinations without parenthesis, this is the only one it finds. – C5H8NNaO4 Jan 02 '17 at 02:35
@TomCarpenter no it would not: a - sign would be missing. – Cœur Jan 02 '17 at 11:36
@Cœur fair point, missed that. Would work for 13-15 as Reti43 said. – Tom Carpenter Jan 02 '17 at 11:47
You used all the integers, and this is the smallest number of characters of course (since it has no parenthesis). You get the tick! – IAmInPLS Jan 02 '17 at 14:44

Oray · Answer 2 · 2017-01-02T11:44:34.680

15

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:

$(10+9×8×7-6-5)×4+3+2×1=2017$ - 22 Chars
$(10×9×8×7)\div((6×5)\div(4×3))+2-1=2017$ - 28 Chars
$10×9×8×7×6\div5\div(4-3+2)+1=2017$ - 22 Chars
$(10+9×8×7-6-5)×4+3+2\div1=2017$ - 22 Chars
$10×9×8×7\div(6+5+4)×3×2+1=2017$ - 22 Chars
$10-9+8×7×6×(5-4)×3×2\div1=2017$ - 22 Chars
$(10-9+8)×7×(6-5+(4-3)×2)+1=2017$ - 26 Chars
$(10+9)×8×(7+6)+5+4×3×(2+1)=2017$ - 26 Chars

edited Jan 02 '17 at 11:44

answered Jan 01 '17 at 13:39

Oray

30,307
6
61
215

2

You can simplify some of those, considering a ÷ (b ÷ c) = a ÷ b × c and a ÷ (b × c) = a ÷ b ÷ c – Daerdemandt Jan 01 '17 at 20:35
2

#3 has mismatching brackets – vrwim Jan 02 '17 at 00:49
Can you include the number of characters for each? – IAmInPLS Jan 02 '17 at 11:17
@IAmInPLS fixed all errors... – Oray Jan 02 '17 at 11:45

score 2 · Answer 3 · answered Jan 01 '17 at 12:07

2

22 characters:

$10×9×8×7×6÷5÷(4−3+2)+1$

There may be less, but pretty happy about this

There is also:

$10×9×8×7×6÷(5+4×3−2)+1$

Which is same length but slightly different

answered Jan 01 '17 at 12:07

Beastly Gerbil

58,036
8
166
314

score 1 · Answer 4 · edited Jan 02 '17 at 18:03

1

(((10*9*8*7)/(6*5))*4*3)+2-1=2017

edited Jan 02 '17 at 18:03

Mithical

8,860
4
36
88

answered Jan 02 '17 at 17:37

user33195

11
1

score 1 · Answer 5 · edited Jan 06 '17 at 06:23

1

2017 = 10+9+8+7+6+5+4+3+2+1+987+654+321

edited Jan 06 '17 at 06:23

stack reader

9,830
1
27
77

answered Jan 06 '17 at 05:56

K S Subramaniam

11
1

While this is a rather interesting result, this is not an answer to the question. – greenturtle3141 Jan 06 '17 at 06:00

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

5 Answers5