What set of positive integers with sum 2024 has highest possible product?
Same question for 2025.
What is the highest product in this century?
Inspired by: Putnam 1979
(In reply to
re: Guesses by Brian Smith)
Right!
As Brian Smith pointed out 3*3 is better than 2*2*2.
Also 3*3*3*1 is better than 5*5 (27 vs 25)
but 3*3*4 is better still (36, vs 27 or 25)
It looks like the optimal set, depending on the mod 3 value of X is:
(let k = integer part of X/3)
if X = 0 mod 3, 3^k
if X = 1 mod 3, 4*3^(k-1)
if X = 2 mod 3, 2*3^(k)
2024: 2*3^674
2025: 3^675
And then depending on which year is the end of the century:
2099: 2*3^699
2100: 3^700
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Posted by Larry
on 2024-03-26 14:27:52 |
re(2): Guesses
