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6 coins (Posted on 2016-01-13) Difficulty: 3 of 5
There are 6 coins weighing 1, 2, 3, 4, 5 and 6 grams that look the same, except for their labels. The labels are supposed to display the weights of the coins.

How can you determine whether all the labels are correct,
using the balance scale only twice?

See The Solution Submitted by Ady TZIDON    
Rating: 4.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution / counterexample | Comment 2 of 10 |
(In reply to Solution by Brian Smith)

There is a third way to weigh 5 coins at once 1+3+4=2+6

but no two of the three works.

Your proposed solution can be foiled if the 
label 1 weighs 5
label 2 weighs 3
label 3 weighs 1
label 4 weighs 6
label 5 weighs 4
label 6 weighs 2

trying {1,2,6} vs {4,5} is 5+3+2=6+4
trying {2,3,5} vs {4,6} is 3+1+4=6+2

there are many possibilities of the form A+B=C+D and so many combinations that I have not tested them all.

Basically I made a spreadsheet of all 720 permutations and comparing pairwise the combos that are valid.

  Posted by Jer on 2016-01-13 12:21:16
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