perplexus.info :: Just Math : Minimizing disjoint sum

Minimizing disjoint sum (Posted on 2023-06-20)

Let A and B be two non-empty subsets of X = {1, 2, . . . , 8 } with A ∪ B = X and A ∩ B = ∅. Let P_A be the product of all elements of A and let P_B be the product of all elements of B. Find the minimum possible value of P_A +P_B.

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 3 of 6 |

clearvars,clc

X=1:8;

best=inf;

for card=1:4

setA=combinator(8,card,'c');

for i=1:length(setA)

A=setA(i,:);

B=setdiff(X,A);

s=prod(A)+prod(B);

if s<best

best=s;

bestA=A;

bestB=B;

end

best

bestA

bestB

finds

best =

402

bestA =

4 6 8

bestB =

1 2 3 5 7

Posted by Charlie on 2023-06-20 14:04:12

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