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No Equal Weighings (Posted on 2016-04-18) Difficulty: 3 of 5
I have a batch of 16 coins, each coin weights either 9g, 10g, or 11g. I split the pile into halves and compare each half on a balance scale and the result is unequal.

Then I take each pile of 8 and perform the same process: split each pile in half and compare the halves from that pile. Both times I get unequal results.

I then repeat the process with the four piles of 4. Again all four weighings are unequal.

I keep going to make eight more weighings comparing the individual coins in each pair formed previously. Again all weighings are unequal.

What are the possible compositions of the original pile of 16 coins?

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: computer solution -- sampling of every 1000th valid sequence | Comment 2 of 4 |
(In reply to computer solution by Charlie)

 9 10 9 11 9 11 11 10 11 10 9 11 11 10 10 9
 9 10 9 11 10 11 9 11 11 9 11 10 11 10 10 9
 9 10 9 11 11 9 11 10 11 9 9 10 11 10 10 9
 9 10 9 11 11 10 11 9 10 11 10 9 10 9 11 9
 9 10 10 11 9 11 10 9 10 11 9 11 11 10 10 9
 9 10 10 11 10 9 11 9 10 9 11 10 11 10 11 9
 9 10 10 11 11 9 10 9 10 9 9 11 11 10 11 9
 9 10 10 11 11 10 11 9 9 11 9 10 11 10 11 9
 9 10 11 9 9 11 11 10 9 10 11 10 10 9 11 9
 9 10 11 9 10 11 9 11 9 10 10 11 10 9 11 9
 9 10 11 9 11 9 10 11 11 10 10 9 11 10 11 9
 9 10 11 9 11 10 10 9 11 10 9 11 10 9 10 11
 9 10 11 10 9 11 9 10 11 9 11 10 10 9 10 11
 9 10 11 10 10 9 9 11 11 9 10 9 11 10 11 9
 9 10 11 10 11 9 9 10 10 11 11 9 10 9 10 11
 9 10 11 10 11 10 9 11 10 9 11 9 10 11 9 11
 9 11 9 10 9 11 10 11 10 9 10 11 11 10 11 9
 9 11 9 10 10 11 9 10 9 11 11 10 11 10 10 9
 9 11 9 10 11 9 10 11 9 11 9 10 11 10 10 9
 9 11 9 10 11 10 10 9 9 10 11 10 11 10 11 9
 9 11 10 9 9 11 10 11 9 10 9 11 11 10 10 9
 9 11 10 9 10 9 11 10 11 10 10 9 11 10 11 9
 9 11 10 9 10 11 11 9 11 10 9 10 10 9 11 9
 9 11 10 9 11 10 9 11 11 9 10 9 11 10 10 9
 9 11 10 11 9 10 10 11 10 11 10 9 11 9 10 9
 9 11 10 11 9 11 10 9 10 11 9 10 11 10 11 9
 9 11 10 11 10 9 11 10 10 9 10 11 11 9 10 9
 9 11 10 11 11 9 10 9 10 9 10 11 10 9 11 9
 9 11 11 10 9 10 10 11 9 11 10 9 10 11 9 11
 9 11 11 10 9 11 10 9 9 10 11 10 11 10 11 9
 9 11 11 10 10 9 11 10 9 10 10 11 11 9 10 9
 9 11 11 10 11 9 9 10 11 10 11 9 11 10 10 9
 10 9 9 11 9 10 10 11 11 10 9 11 11 10 10 9
 10 9 9 11 10 9 10 11 11 9 11 10 11 10 10 9
 10 9 9 11 10 11 10 9 11 9 10 11 10 9 10 11
 10 9 9 11 11 10 9 10 10 11 11 9 11 10 10 9
 10 9 10 11 9 10 9 11 10 11 9 11 11 10 10 9
 10 9 10 11 9 11 10 11 10 9 9 11 11 10 11 9
 10 9 10 11 10 11 9 11 9 11 10 11 11 9 10 9
 10 9 10 11 11 9 10 11 9 11 9 10 11 10 11 9
 10 9 11 9 9 10 10 11 9 11 9 10 11 10 11 9
 10 9 11 9 10 9 10 11 9 10 10 11 11 10 11 9
 10 9 11 9 10 11 9 11 11 10 10 9 11 10 11 9
 10 9 11 9 11 9 11 10 11 10 9 10 11 10 11 9
 10 9 11 9 11 10 11 9 11 9 10 11 11 10 10 9
 10 9 11 10 9 11 10 9 11 9 10 9 11 10 11 9
 10 9 11 10 10 9 11 9 10 11 11 9 10 9 10 11
 10 9 11 10 11 9 10 9 10 11 9 11 10 9 10 11
 10 9 11 10 11 10 11 9 10 9 9 11 10 11 9 11
 10 11 9 10 9 11 10 9 9 11 11 10 11 10 10 9
 10 11 9 10 10 9 11 9 9 11 10 11 10 9 10 11
 10 11 9 10 11 9 10 9 9 10 11 10 11 10 11 9
 10 11 9 10 11 10 11 9 9 10 9 11 10 11 9 11
 10 11 9 11 9 10 11 9 11 10 10 9 10 9 11 9
 10 11 9 11 10 9 9 11 11 10 9 10 10 9 11 9
 10 11 9 11 10 11 9 10 11 9 9 10 11 10 11 9
 10 11 9 11 11 10 9 10 10 11 10 9 11 9 10 9
 10 11 10 9 9 11 9 10 10 11 10 9 11 10 11 9
 10 11 10 9 10 9 9 11 10 11 9 10 11 10 11 9
 10 11 10 9 11 9 9 10 10 9 10 11 11 10 11 9
 10 11 10 9 11 10 9 11 9 11 10 9 10 11 9 11
 10 11 11 9 9 10 11 9 9 10 11 10 11 10 11 9
 10 11 11 9 10 9 9 11 9 10 10 11 11 10 11 9
 10 11 11 9 10 9 11 10 11 10 11 9 11 9 10 9
 10 11 11 9 11 9 10 9 11 10 9 11 11 10 10 9
 11 9 9 10 9 10 11 10 11 9 11 10 11 10 10 9
 11 9 9 10 10 9 11 10 11 9 10 11 10 9 10 11
 11 9 9 10 10 11 11 9 10 11 10 9 10 9 11 9
 11 9 9 10 11 10 9 11 10 11 9 10 10 9 11 9
 11 9 10 9 9 10 11 10 10 9 11 10 11 10 11 9
 11 9 10 9 10 9 11 10 10 9 9 11 11 10 11 9
 11 9 10 9 10 11 11 9 9 11 10 9 11 10 10 9
 11 9 10 9 11 10 9 11 9 10 11 10 10 9 11 9
 11 9 10 11 9 10 10 11 9 10 9 11 11 10 11 9
 11 9 10 11 9 11 9 10 11 10 10 9 11 10 11 9
 11 9 10 11 10 9 11 9 11 10 9 10 11 10 11 9
 11 9 10 11 11 9 9 10 11 9 10 11 11 10 10 9
 11 9 11 10 9 10 9 11 10 11 11 9 11 10 10 9
 11 9 11 10 9 11 9 10 10 11 9 11 11 10 10 9
 11 9 11 10 10 9 11 9 10 9 11 10 11 10 11 9
 11 9 11 10 11 9 9 10 10 9 10 11 11 10 11 9
 11 10 9 10 9 10 9 11 9 11 11 10 11 10 10 9
 11 10 9 10 9 11 10 11 9 11 9 10 10 11 9 11
 11 10 9 10 10 11 9 11 9 10 11 9 10 11 9 11
 11 10 9 10 11 9 10 11 9 10 9 11 10 11 9 11
 11 10 9 10 11 10 11 9 11 10 9 11 11 9 10 9
 11 10 9 11 9 10 11 10 11 9 10 11 11 9 10 9
 11 10 9 11 10 9 10 11 11 9 9 10 11 10 11 9
 11 10 9 11 10 11 10 9 10 11 10 9 11 9 10 9
 11 10 9 11 11 10 10 9 10 9 11 10 11 9 10 9
 11 10 10 9 9 11 10 9 10 11 9 10 11 10 11 9
 11 10 10 9 10 9 11 9 10 9 10 11 11 10 11 9
 11 10 10 9 11 9 10 9 9 11 11 10 10 9 10 11
 11 10 10 9 11 10 11 9 9 10 11 10 11 9 10 9
 11 10 11 9 9 10 11 10 9 10 10 11 11 9 10 9
 11 10 11 9 10 9 9 11 11 10 11 9 11 10 10 9
 11 10 11 9 10 11 9 10 11 10 9 10 11 9 10 9
 11 10 11 9 11 10 9 10 11 9 10 9 11 10 11 9

For example, in the last set, there were six 11's and five of each of 9 and 10.

  Posted by Charlie on 2016-04-18 15:10:27
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