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27 Weights (Posted on 2003-05-31) Difficulty: 3 of 5
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 ?

See The Solution Submitted by Ravi Raja    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: First answer: | Comment 2 of 15 |
(In reply to First answer: by Gamer)

7² should be in the second pile.

a) I used 1²,5²,9²,12²13²,17²,20²,24²,25² in one pile, 2²,6²,7²,10²,14²,18²,21²,22²,26² in the next pile, and 3², 4², 8², 11², 15², 16², 19², 23², 27² in the last pile.

The way this works is distribute the squares (like cards) into 3 piles during 3 rounds of "sets" each. (1² is at the top of the stack and 27² is at the bottom of the stack)

In each "set" it goes ABC, BCA, or CAB.

The "Start with _" rounds go ACB, BAC, or CBA.

What you start with at the beginning of each round goes ABC, BCA or CAB.

(Assuming you call the first pile you deal to A)

Set 1: Start with A==01 02 03
Set 2: Start with C==05 06 04
Set 3: Start with B==09 07 08

Set 4: Start with B==12 10 11
Set 5: Start with A==13 14 15
Set 6: Start with C==17 18 16

Set 7: Start with C==20 21 19
Set 8: Start with B==24 22 23
Set 9: Start with A==25 26 27

So the pattern goes ABCBCACABCABABCBCABCACABABC
  Posted by Gamer on 2003-05-31 07:21:14

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