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 ?

^{x=1 to 27} SIGMA x² = 6930.

(a) One set of three groups [6930/3 = 2310] is as follows:
2310 = 1², 3², 5², 6², 9², 13², 20², 22², 23², 24²
2310 = 2², 4², 8², 14², 25², 26², 27²
2310 = 7², 10², 11², 12², 15², 16², 17², 18², 19², 21²

(b) Yes. A set of five groups [6930/5 = 1366] is as follows:
1366 = 1², 16², 20², 27²
1366 = 2², 9², 25², 26²
1366 = 3², 4², 5², 6², 8², 10², 11², 13², 14², 17², 19²
1366 = 7², 18², 22², 23²
1366 = 12², 15², 21², 24²

Posted by Dej Mar on 2007-12-04 10:58:12