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Five numbers and Six sums (Posted on 2020-12-20) Difficulty: 4 of 5
A set of five numbers are added in all 10 possible pairs like in some of the Pumpkins puzzles.

When sorted the middle six sums are 47, 48, 50, 51, 52, and 54. The two largest sums and two smallest sums are not given, similar to Permuted Sums.

What are the possible sets of the five original numbers?

See The Solution Submitted by Brian Smith    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Another possibility Comment 5 of 5 |
(In reply to Another possibility by Steve Herman)

If variable a is started at 1.5 instead of 1, the other variables follow suit in being offset by .5, resulting in:


 19.5    23.5    24.5    27.5    30.5
    43    44    47    50    48    51    54    52    55    58 orig sums
    43    44    47    48    50    51    52    54    55    58 sorted sums
 
 19.5    23.5    26.5    27.5    28.5
    43    46    47    48    50    51    52    54    55    56
    43    46    47    48    50    51    52    54    55    56

Other fractions would be more problematic to program, and I think make solution impossible as, for example a .6 would have to be paired with a .4, but then later, two of these .6's would have to be paired with each other.


Edited on December 23, 2020, 10:59 am
  Posted by Charlie on 2020-12-23 10:55:41

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