Consider a sequence of integers in arithmetical progression: A, A+B, A+2B, A+3B, ... A+NB.

Systematically pick any two adjacent numbers, and randomly replace them by their sum or difference. Keep at this until only one number remains. Is this number odd or even? What's the largest value this number can attain?

(In reply to solution by Charlie)

Hey Charlie:

I totally follow your proof and get it and agree.  Could you help me understand something about my approach though?  I got the same equation for the full sum as you did, but I didn't factor out the (N+1).

Where did I go wrong in the two cases where both N and B are odd?  In those cases (N+1)A will always be even, so the evenness of the sum depends on N(N+1)B/2 (if it's even then the sum is even, if it's odd then the sum is odd)

Hmmm, I confused myself.  I'd appreciate any enlightenment.

Thanks!

Posted by nikki on 2004-10-01 11:45:22