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?
(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.
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Posted by Jer
on 2016-01-13 12:21:16 |
re: Solution / counterexample
