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.)

(In reply to

re(2): Counting Up by Charlie)

My way:

I have solved it rather quickly, counting from both ends, using the following logic:

a.Clearly both 1 and 20 must be in the solution, otherwise the puzzle would address a shorter range of numbers.

b. Start coverging from both direction toward the middle:-

chose delta=1 on one end (say the begining) and=2 on the other.

**1 2.....18 20** (later by replacing each member** m** by **21-m** we will have another valid solution)

Now my task (so would be the computer task - but who cares?)became significantly easier - the (1,2 )delta set can be applied only in one way , got a dead end - tried (2,2) and (1,3)etc

and after short fiddling with **(4,3)==> 1 2 6 ...15 18 20**

got the solution** ** **1 2 6 7 9 14 15 18 20.**

Stopped here,

realising that there is at least one more symmetrical solution.

*Edited on ***April 9, 2013, 1:24 am**