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.
(In reply to Another Analytic Solution
by Brian Smith)
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