How many numbers, from 1 to 50 (both included) can you arrange in a row (one of each) so that each one, except the first and the last, is the sum or difference of its two neighbours?

Example: 3, 10, 7, 17, 24, 41.

10 = 3+7, 7 = 17-10, 17 = 24-7, 24 = 41-17.

There are two set of numbers which are in conformity with the provisions inclusive of the problem uner reference, and these are:

(49, 30, 19, 11, 8, 3, 5, 2, 7, 9, 16, 25, 41), and:
 (41, 25, 16, 9, 7,2,5,3,8,11,19,30,49).

Edited on January 7, 2009, 12:24 pm

Posted by K Sengupta on 2009-01-07 12:03:03