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 part b by Charlie)

As 6930/10=693 < 27², there's no way of doing this for 10 or more groups. That leave 5, 6, 7 and 9 as possibilities, of which the program found solutions for 5, but none for 6 or 7. I haven't tried 9.

Posted by Charlie on 2003-05-31 11:46:07