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?
(In reply to
proposed solution by Charlie)
I believe Charlie's solution is indeed the best. Consider:
WOLG let a<b<c. If a is 3 or greater, then no trio can sum to greater than 1/3+1/4+1/5=0.78333....
So a=2. If b>3, then the best solution is 1/2+1/4+1/5=0.95.
So a=2 and b=3. Brute force shows c=5 to be the best answer.
This is Charlie's answer.
Edited on December 23, 2024, 1:34 pm
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Posted by Kenny M
on 2024-12-23 10:42:06 |
re: proposed solution - the best possible?
