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
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.
realising that there is at least one more symmetrical solution.
Edited on April 9, 2013, 1:24 am