Project Euler Forum

In the problem description of Problem 374 (View Problem) the following statements are given

Partitions that differ only in the order of their summands are considered the same. A partition of n into distinct parts is a partition of n in which every part occurs at most once.

and

For n=10 the partition with the largest product is 10=2+3+5, which gives f(10)=30 and m(10)=3.
And their product, f(10)·m(10) = 30·3 = 90

Whats wrong with this alternative partition of 10? Another question is, since should be a function what is the result of partition e.g. 4? Thanks,
Andreas

agebhar1 wrote:Whats wrong with this alternative partition of 10?
10 = 2+2+3+3 -> f(10) = 36, m(10) = 4

This:

Problem 374 wrote:Let f(n) be the maximum product of the parts of any such partition of n into distinct parts

agebhar1 wrote:Another question is, since m should be a function what is the result of partition e.g. 4?
4 = 4 -> f(4) = 4, m(4) = 1
4 = 2+2 -> f(4) = 4, m(4) = 2

I don't think m will be ambiguous if you have distinct parts in the maximum product.

Problem 374 wrote:Let f(n) be the maximum product of the parts of any such partition of n into distinct parts

I missunderstood distinct. I thought it refers to the order of summands of the partition.

Thanks for the clarification.
Andreas