Suppose you have 27 weights weighing: 1², 2², 3², 4², ........, 25², 26² and 27² grams respectively.

(a)How can you group them into three groups so that each group has the same weight ?

(b) Is it possible to divide it into more than three groups satisfying the same conditions ?

(In reply to re: part b by Charlie)

After fixing a bug in my program for 7 groups, I find that there are 1029 ways of arranging the weights into 7 groups with equal weight. One such is
4², 8², 9², 10², 27²
3², 7², 16², 26²
13², 14², 25²
2², 11², 17², 24²
5², 6², 20², 23²
1², 12², 19², 22²
15², 18², 21²

Posted by Charlie on 2003-05-31 16:15:51