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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)

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Solution MATLAB solution | Comment 2 of 5 |
for a=1:53
    s(1)=a;
    for b=a:53
        s(2)=b;
        for c=b:53
            s(3)=c;
            for d=c:53
                s(4)=d;
                for e=d:53
                    s(5)=e;
                    comb=nchoosek(s,2);
                    for i=1:length(comb)
                        t(i)=sum(comb(i,:));
                    end
                    tOrig=t;
                    t=sort(t);
                    test=t(3:8);
                    if test==[47 48 50 51 52 54]
                        disp(s) 
                        disp(tOrig)
                        disp(t)
                        disp(" ")
                    end
                end
            end
        end
    end
end    
finds    

    20    23    25    27    31
    43    45    47    51    48    50    54    52    56    58
    43    45    47    48    50    51    52    54    56    58
 
    21    23    24    27    31
    44    45    48    52    47    50    54    51    55    58
    44    45    47    48    50    51    52    54    55    58  
    
as the two possibilities for the set of five original numbers listed in numeric order.   Each is followed by the sums in the order found, and then in sorted order, the original order being a+b, ..., a+e, b+c, ..., b+e, ..., c+d, ..., c+e, d+e. 

  Posted by Charlie on 2020-12-20 11:22:22
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