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 Pumpkins 3 (Posted on 2014-01-22)
This is in continuation of Pumpkins and Pumpkins 2.

Six pumpkins - each having a different weight - are weighed two at a time in all 15 sets of two. The weights are recorded as: 27, 36, 39, 45, 48, 51, 54, 57, 63, 66, 72, 75 and 81 pounds.
• Precisely two of the values occurred exactly twice, but these values were only written down once.
• Each of the individual weights (in pounds) is a positive integer.
Derive the weights of the pumpkins and which two values occur twice.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 re: Another Analytic Solution | Comment 5 of 6 |
(In reply to Another Analytic Solution by Brian Smith)

Brian:

I was ready to nominate you as the pumpkin master, but your case 3 solution fails.

It has three duplicate weighings, 41 and 63 and 54, and nothing that totals 51.
54 = 9 + 45 = 18 + 36

 Posted by Steve Herman on 2016-01-26 11:03:11

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