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 re: solution by nikki)

It is because your solution is correct, while mine is incorrect.

I hastily noted that when N is odd, that N+1 was even, and assumed that would result in my product being even, neglecting the fact that the other factor could be a fraction--an odd multiple of 1/2.  You correctly differentiate those cases where N+1 is or is not a multiple of 4.  When it is a multiple of 4, that obviates any fractional (odd halves) value that the other factor may have, but when it is not, then it cannot turn the whole value even, just integral.

Posted by Charlie on 2004-10-01 12:23:20