perplexus.info :: Just Math : Closest to 1

Closest to 1 (Posted on 2024-12-23)

a, b, c are three distinct whole numbers. How close can 1/a+1/b+1/c be to 1 while being still less than it?

No Solution Yet Submitted by Danish Ahmed Khan

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proposed solution

| Comment 1 of 4

univ=2:200;

idx=combinator(length(univ),3,'c');

sets=univ(idx);

mx=0;

for i=1:length(sets)

s=sets(i,:);

p=prod(s);

if s(1)*s(2)+s(3)*s(2)+s(1)*s(3)<p % all integer avoids rounding error

v=sum(1./s);

if v>mx

mx=v;

best=s;

end

best

finds a, b, c and the total of 1/a + 1/b + 1/c:

best =

2 3 7

mx =

0.976190476190476

1/52 short of 1.

Posted by Charlie on 2024-12-23 08:52:49

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