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 ?
Pile1; 1²,5²,9²,12²13²,17²,20²,24²,25²
Pile2: 2²,6²,7²,10²,14²,18²,21²,22²,26²
Pile 3: 3², 4², 8², 11², 15², 16², 19², 23², 27²