perplexus.info :: General : Non-arithmetic Triplets

Non-arithmetic Triplets (Posted on 2013-04-08)

Find nine different integers from 1 to 20 inclusive such that no combination of any three of the nine integers form an arithmetic sequence.

(For example, if two of the integers chosen were 7 and 13, then that would preclude 1, 10 and 19 from being included.)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re(2): Counting Up

| Comment 4 of 9 |

(In reply to re: Counting Up by Jer)

Yes, there are a lot of dead ends and backup and advance situations before hitting on a solution, making the computer's use of the technique more of a pleasure:

1 2 4 5 10 11 13 14
1 2 4 5 10 11 14
1 2 4 5 10 12 13 17
1 2 4 5 10 12 17
1 2 4 5 10 13 14 17
1 2 4 5 10 13 14 20
1 2 4 5 10 13 17 20
1 2 4 5 10 13 20
1 2 4 5 10 14 17
1 2 4 5 10 14 20
1 2 4 5 10 17 20
1 2 4 5 10 20
1 2 4 5 11 12 14 15
1 2 4 5 11 12 15 16
1 2 4 5 11 12 16
1 2 4 5 11 13 14 16
1 2 4 5 11 13 14 19
1 2 4 5 11 13 16
1 2 4 5 11 13 19
1 2 4 5 11 14 15
1 2 4 5 11 14 16 19
1 2 4 5 11 14 19
1 2 4 5 11 15 16
1 2 4 5 11 16 19
1 2 4 5 11 19
1 2 4 5 12 13 15 16
1 2 4 5 12 13 16 17
1 2 4 5 12 13 16 18
1 2 4 5 12 13 17 18
1 2 4 5 12 13 18
1 2 4 5 12 14 15 17
1 2 4 5 12 14 17 18
1 2 4 5 12 14 18
1 2 4 5 12 15 16
1 2 4 5 12 15 17
1 2 4 5 12 16 17
1 2 4 5 12 16 18
1 2 4 5 12 17 18
1 2 4 5 12 18
1 2 4 5 13 14 16 17
1 2 4 5 13 14 16 20
1 2 4 5 13 14 17 18
1 2 4 5 13 14 17 19
1 2 4 5 13 14 18 19
1 2 4 5 13 14 18 20
1 2 4 5 13 14 19 20
1 2 4 5 13 14 20
1 2 4 5 13 15 16 18
1 2 4 5 13 15 16 20
1 2 4 5 13 15 18 19
1 2 4 5 13 15 18 20
1 2 4 5 13 15 19 20
1 2 4 5 13 15 20
1 2 4 5 13 16 17 20
1 2 4 5 13 16 18
1 2 4 5 13 16 20
1 2 4 5 13 17 18 20
1 2 4 5 13 17 19 20
1 2 4 5 13 17 20
1 2 4 5 13 18 19
1 2 4 5 13 18 20
1 2 4 5 13 19 20
1 2 4 5 13 20
1 2 4 5 14 15 17 18
1 2 4 5 14 15 18 19
1 2 4 5 14 15 18 20
1 2 4 5 14 15 19 20
1 2 4 5 14 15 20
1 2 4 5 14 16 17 19
1 2 4 5 14 16 19 20
1 2 4 5 14 16 20
1 2 4 5 14 17 18
1 2 4 5 14 17 19
1 2 4 5 14 18 19
1 2 4 5 14 18 20
1 2 4 5 14 19 20
1 2 4 5 14 20
1 2 4 5 15 16 18 19
1 2 4 5 15 16 19 20
1 2 4 5 15 16 20
1 2 4 5 15 17 18 20
1 2 4 5 15 17 20
1 2 4 5 15 18 19
1 2 4 5 15 18 20
1 2 4 5 15 19 20
1 2 4 5 15 20
1 2 4 5 16 17 19 20
1 2 4 5 16 17 20
1 2 4 5 16 18 19
1 2 4 5 16 19 20
1 2 4 5 16 20
1 2 4 5 17 18 20
1 2 4 5 17 19 20
1 2 4 5 17 20
1 2 4 5 18 19
1 2 4 5 18 20
1 2 4 5 19 20
1 2 4 5 20
1 2 4 8 9 11 19
1 2 4 8 9 13 19 20
1 2 4 8 9 13 20
1 2 4 8 9 18 19
1 2 4 8 9 18 20
1 2 4 8 9 19 20
1 2 4 8 9 20
1 2 4 8 10 11 13 17
1 2 4 8 10 11 17
1 2 4 8 10 13 17 20
1 2 4 8 10 13 20
1 2 4 8 10 17 20
1 2 4 8 10 20
1 2 4 8 11 13 16 17
1 2 4 8 11 13 17 19
1 2 4 8 11 13 19
1 2 4 8 11 16 17 19
1 2 4 8 11 16 19
1 2 4 8 11 17 19
1 2 4 8 11 19
1 2 4 8 13 16 17 20
1 2 4 8 13 16 20
1 2 4 8 13 17 19 20
1 2 4 8 13 17 20
1 2 4 8 13 19 20
1 2 4 8 13 20
1 2 4 8 16 17 19 20
1 2 4 8 16 17 20
1 2 4 8 16 18 19
1 2 4 8 16 19 20
1 2 4 8 16 20
1 2 4 8 17 18 20
1 2 4 8 17 19 20
1 2 4 8 17 20
1 2 4 8 18 19
1 2 4 8 18 20
1 2 4 8 19 20
1 2 4 8 20
1 2 4 9 10 12 13
1 2 4 9 10 13 15
1 2 4 9 10 13 20
1 2 4 9 10 15
1 2 4 9 10 20
1 2 4 9 11 12 19
1 2 4 9 11 15
1 2 4 9 11 19
1 2 4 9 12 13 18 19
1 2 4 9 12 13 19
1 2 4 9 12 18 19
1 2 4 9 12 19
1 2 4 9 13 15 18 19
1 2 4 9 13 15 18 20
1 2 4 9 13 15 19 20
1 2 4 9 13 15 20
1 2 4 9 13 18 19
1 2 4 9 13 18 20
1 2 4 9 13 19 20
1 2 4 9 13 20
1 2 4 9 15 18 19
1 2 4 9 15 18 20
1 2 4 9 15 19 20
1 2 4 9 15 20
1 2 4 9 18 19
1 2 4 9 18 20
1 2 4 9 19 20
1 2 4 9 20
1 2 4 10 11 13 14
1 2 4 10 11 13 17
1 2 4 10 11 14 15
1 2 4 10 11 15 17
1 2 4 10 11 17
1 2 4 10 12 13 15
1 2 4 10 12 13 17
1 2 4 10 12 15 17
1 2 4 10 12 17
1 2 4 10 13 14 17
1 2 4 10 13 14 20
1 2 4 10 13 15
1 2 4 10 13 17 20
1 2 4 10 13 20
1 2 4 10 14 15 17
1 2 4 10 14 17
1 2 4 10 14 20
1 2 4 10 15 17
1 2 4 10 17 20
1 2 4 10 20
1 2 4 11 12 14 15
1 2 4 11 12 14 19
1 2 4 11 12 15 16
1 2 4 11 12 15 17
1 2 4 11 12 16 17 19
1 2 4 11 12 16 19
1 2 4 11 12 17 19
1 2 4 11 12 19
1 2 4 11 13 14 16
1 2 4 11 13 14 19
1 2 4 11 13 16 17
1 2 4 11 13 17 19
1 2 4 11 13 19
1 2 4 11 14 15
1 2 4 11 14 16 19
1 2 4 11 14 19
1 2 4 11 15 16
1 2 4 11 15 17
1 2 4 11 16 17 19
1 2 4 11 16 19
1 2 4 11 17 19
1 2 4 11 19
1 2 4 12 13 15 16
1 2 4 12 13 15 19
1 2 4 12 13 16 17
1 2 4 12 13 16 18
1 2 4 12 13 17 18
1 2 4 12 13 17 19
1 2 4 12 13 18 19
1 2 4 12 13 19
1 2 4 12 14 15 17
1 2 4 12 14 15 19
1 2 4 12 14 17 18
1 2 4 12 14 17 19
1 2 4 12 14 18 19
1 2 4 12 14 19
1 2 4 12 15 16 19
1 2 4 12 15 17
1 2 4 12 15 19
1 2 4 12 16 17 19
1 2 4 12 16 18 19
1 2 4 12 16 19
1 2 4 12 17 18
1 2 4 12 17 19
1 2 4 12 18 19
1 2 4 12 19
1 2 4 13 14 16 17
1 2 4 13 14 16 20
1 2 4 13 14 17 18
1 2 4 13 14 17 19
1 2 4 13 14 18 19
1 2 4 13 14 18 20
1 2 4 13 14 19 20
1 2 4 13 14 20
1 2 4 13 15 16 18
1 2 4 13 15 16 20
1 2 4 13 15 18 19
1 2 4 13 15 18 20
1 2 4 13 15 19 20
1 2 4 13 15 20
1 2 4 13 16 17 20
1 2 4 13 16 18
1 2 4 13 16 20
1 2 4 13 17 18 20
1 2 4 13 17 19 20
1 2 4 13 17 20
1 2 4 13 18 19
1 2 4 13 18 20
1 2 4 13 19 20
1 2 4 13 20
1 2 4 14 15 17 18
1 2 4 14 15 18 19
1 2 4 14 15 18 20
1 2 4 14 15 19 20
1 2 4 14 15 20
1 2 4 14 16 17 19
1 2 4 14 16 19 20
1 2 4 14 16 20
1 2 4 14 17 18
1 2 4 14 17 19
1 2 4 14 18 19
1 2 4 14 18 20
1 2 4 14 19 20
1 2 4 14 20
1 2 4 15 16 18 19
1 2 4 15 16 19 20
1 2 4 15 16 20
1 2 4 15 17 18 20
1 2 4 15 17 20
1 2 4 15 18 19
1 2 4 15 18 20
1 2 4 15 19 20
1 2 4 15 20
1 2 4 16 17 19 20
1 2 4 16 17 20
1 2 4 16 18 19
1 2 4 16 19 20
1 2 4 16 20
1 2 4 17 18 20
1 2 4 17 19 20
1 2 4 17 20
1 2 4 18 19
1 2 4 18 20
1 2 4 19 20
1 2 4 20
1 2 5 6 12 13 15 16
1 2 5 6 12 13 16 17
1 2 5 6 12 13 17
1 2 5 6 12 14 15 17
1 2 5 6 12 14 15 20
1 2 5 6 12 14 17
1 2 5 6 12 14 20
1 2 5 6 12 15 16
1 2 5 6 12 15 17 20
1 2 5 6 12 15 20
1 2 5 6 12 16 17
1 2 5 6 12 17 20
1 2 5 6 12 20
1 2 5 6 13 14 16 17
1 2 5 6 13 14 17 18
1 2 5 6 13 14 17 19
1 2 5 6 13 14 18 19
1 2 5 6 13 14 19
1 2 5 6 13 15 16 18
1 2 5 6 13 15 18 19
1 2 5 6 13 15 19
1 2 5 6 13 16 17
1 2 5 6 13 16 18
1 2 5 6 13 17 18
1 2 5 6 13 17 19
1 2 5 6 13 18 19
1 2 5 6 13 19
1 2 5 6 14 15 17 18
1 2 5 6 14 15 18 19
1 2 5 6 14 15 18 20
1 2 5 6 14 15 19 20
1 2 5 6 14 15 20
1 2 5 6 14 16 17 19
1 2 5 6 14 16 19 20
1 2 5 6 14 16 20
1 2 5 6 14 17 18
1 2 5 6 14 17 19
1 2 5 6 14 18 19
1 2 5 6 14 18 20
1 2 5 6 14 19 20
1 2 5 6 14 20
1 2 5 6 15 16 18 19
1 2 5 6 15 16 19 20
1 2 5 6 15 16 20
1 2 5 6 15 17 18 20
1 2 5 6 15 17 20
1 2 5 6 15 18 19
1 2 5 6 15 18 20
1 2 5 6 15 19 20
1 2 5 6 15 20
1 2 5 6 16 17 19 20
1 2 5 6 16 17 20
1 2 5 6 16 18 19
1 2 5 6 16 19 20
1 2 5 6 16 20
1 2 5 6 17 18 20
1 2 5 6 17 19 20
1 2 5 6 17 20
1 2 5 6 18 19
1 2 5 6 18 20
1 2 5 6 19 20
1 2 5 6 20
1 2 5 7 10 11 14 16
1 2 5 7 10 11 16
1 2 5 7 10 14 16 17
1 2 5 7 10 14 16 20
1 2 5 7 10 14 17
1 2 5 7 10 14 20
1 2 5 7 10 16 17 20
1 2 5 7 10 16 20
1 2 5 7 10 17 20
1 2 5 7 10 20
1 2 5 7 11 14 16 19
1 2 5 7 11 14 18 19
1 2 5 7 11 14 19
1 2 5 7 11 16 18 19
1 2 5 7 11 16 19
1 2 5 7 11 18 19
1 2 5 7 11 19
1 2 5 7 14 15 17 18
1 2 5 7 14 15 18 19
1 2 5 7 14 15 18 20
1 2 5 7 14 15 19 20
1 2 5 7 14 15 20
1 2 5 7 14 16 17 19
1 2 5 7 14 16 19 20
1 2 5 7 14 16 20
1 2 5 7 14 17 18
1 2 5 7 14 17 19
1 2 5 7 14 18 19
1 2 5 7 14 18 20
1 2 5 7 14 19 20
1 2 5 7 14 20
1 2 5 7 15 16 18 19
1 2 5 7 15 16 19 20
1 2 5 7 15 16 20
1 2 5 7 15 17 18 20
1 2 5 7 15 17 20
1 2 5 7 15 18 19
1 2 5 7 15 18 20
1 2 5 7 15 19 20
1 2 5 7 15 20
1 2 5 7 16 17 19 20
1 2 5 7 16 17 20
1 2 5 7 16 18 19
1 2 5 7 16 19 20
1 2 5 7 16 20
1 2 5 7 17 18 20
1 2 5 7 17 19 20
1 2 5 7 17 20
1 2 5 7 18 19
1 2 5 7 18 20
1 2 5 7 19 20
1 2 5 7 20
1 2 5 10 11 13 14
1 2 5 10 11 14 16
1 2 5 10 11 16
1 2 5 10 12 13 17 20
1 2 5 10 12 13 20
1 2 5 10 12 16 17
1 2 5 10 12 17 20
1 2 5 10 12 20
1 2 5 10 13 14 17
1 2 5 10 13 14 20
1 2 5 10 13 17 20
1 2 5 10 13 20
1 2 5 10 14 16 17
1 2 5 10 14 16 20
1 2 5 10 14 17
1 2 5 10 14 20
1 2 5 10 16 17 20
1 2 5 10 16 20
1 2 5 10 17 20
1 2 5 10 20
1 2 5 11 12 14 15
1 2 5 11 12 14 18
1 2 5 11 12 15 16
1 2 5 11 12 16 18
1 2 5 11 12 18
1 2 5 11 13 14 16
1 2 5 11 13 14 18 19
1 2 5 11 13 14 19
1 2 5 11 13 16 18
1 2 5 11 13 18 19
1 2 5 11 13 19
1 2 5 11 14 15 18
1 2 5 11 14 16 19
1 2 5 11 14 18 19
1 2 5 11 14 19
1 2 5 11 15 16 18
1 2 5 11 15 18
1 2 5 11 16 18 19
1 2 5 11 16 19
1 2 5 11 18 19
1 2 5 11 19
1 2 5 12 13 15 16
1 2 5 12 13 15 20
1 2 5 12 13 16 17
1 2 5 12 13 16 18
1 2 5 12 13 17 18 20
1 2 5 12 13 17 20
1 2 5 12 13 18 20
1 2 5 12 13 20
1 2 5 12 14 15 17
1 2 5 12 14 15 20
1 2 5 12 14 17 18
1 2 5 12 14 18 20
1 2 5 12 14 20
1 2 5 12 15 16
1 2 5 12 15 17 20
1 2 5 12 15 20
1 2 5 12 16 17
1 2 5 12 16 18
1 2 5 12 17 18 20
1 2 5 12 17 20
1 2 5 12 18 20
1 2 5 12 20
1 2 5 13 14 16 17
1 2 5 13 14 16 20
1 2 5 13 14 17 18
1 2 5 13 14 17 19
1 2 5 13 14 18 19
1 2 5 13 14 18 20
1 2 5 13 14 19 20
1 2 5 13 14 20
1 2 5 13 15 16 18
1 2 5 13 15 16 20
1 2 5 13 15 18 19
1 2 5 13 15 18 20
1 2 5 13 15 19 20
1 2 5 13 15 20
1 2 5 13 16 17 20
1 2 5 13 16 18
1 2 5 13 16 20
1 2 5 13 17 18 20
1 2 5 13 17 19 20
1 2 5 13 17 20
1 2 5 13 18 19
1 2 5 13 18 20
1 2 5 13 19 20
1 2 5 13 20
1 2 5 14 15 17 18
1 2 5 14 15 18 19
1 2 5 14 15 18 20
1 2 5 14 15 19 20
1 2 5 14 15 20
1 2 5 14 16 17 19
1 2 5 14 16 19 20
1 2 5 14 16 20
1 2 5 14 17 18
1 2 5 14 17 19
1 2 5 14 18 19
1 2 5 14 18 20
1 2 5 14 19 20
1 2 5 14 20
1 2 5 15 16 18 19
1 2 5 15 16 19 20
1 2 5 15 16 20
1 2 5 15 17 18 20
1 2 5 15 17 20
1 2 5 15 18 19
1 2 5 15 18 20
1 2 5 15 19 20
1 2 5 15 20
1 2 5 16 17 19 20
1 2 5 16 17 20
1 2 5 16 18 19
1 2 5 16 19 20
1 2 5 16 20
1 2 5 17 18 20
1 2 5 17 19 20
1 2 5 17 20
1 2 5 18 19
1 2 5 18 20
1 2 5 19 20
1 2 5 20
1 2 6 7 9 14 15 18 20

Posted by Charlie on 2013-04-08 19:56:32

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