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Non-arithmetic Triplets (Posted on 2013-04-08) Difficulty: 3 of 5
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.)

No Solution Yet Submitted by K Sengupta    
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re(4): Counting Up,,,,Why not up and down? | Comment 7 of 9 |
(In reply to re(3): Counting Up,,,,Why not up and down? by Ady TZIDON)

How would you know to start with a difference of 1 at one end and 2 at the other?

If for example the puzzle asked for 12 different integers from 1 to 30, you'd want

1, 3, 4, 8, 9, 11, 20, 22, 23, 27, 28, 30

with a difference of 2 at each end. In this case it's its own mirror structure.

Also, as another example, the following are the reversable kind, but still has a difference of 1 at each end, as the asymmetry is farther in:

Thirteen out of 32:

1, 2, 4, 8, 9, 11, 19, 22, 23, 26, 28, 31,32

1, 2, 5, 7, 10, 11, 14, 22, 24, 25, 29, 31, 32

Edited on April 9, 2013, 1:57 am
  Posted by Charlie on 2013-04-09 01:52:20

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