Problem 088

[satyres]

Why this is wrong?
k=2: 2 = 2 × 1 = 1 + 1
Thanks !

[jaap]

Why this is wrong?
k=2: 2 = 2 × 1 = 1 + 1
Thanks !

You need the same numbers in the product as in the sum. So 1x1 and 1+1, or 2x1 and 2+1, but neither of these are correct.

[nicolas.patrois]

The lists must be the same and 2+1≠1×1. You must have x+y=x×y.

[satyres]

Thanks both for the clarification ! really apreciate it !

[tomboy]

Hello.

I'm positive I've understood the problem and got a good algorithm in my head. Still, it spits out a wrong result for the second example in the problem: Instead of {4, 6, 8, 12, 15, 16} I get {4, 6, 8, 12, 15, 16, 20} for the minimal product-sums 2<=k<=12.

In particular, it's the minimal product-sum for 10 I'm stuck on. My algorithm (verified by hand) says its minimum prod-sum is 20. What is the real answer? I just can't find something smaller.

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[nicolas.patrois]

I find 16.

[tomboy]

As usual, i got my counting wrong.
Thanks

[syckls]

The problem statement says, "A natural number, N, that can be written as the sum and product of a given set of at least two natural numbers, {a1, a2, ... , ak} is called a product-sum number." However, several of the examples given have repeated numbers. I think the problem statement should say, "A natural number, N, that can be written as the sum and product of a given sequence a1, a2, ... , ak of at least two natural numbers, is called a product-sum number."

[hk]

The mathematical name of the structure you mean is Multiset

[syckls]

"Multiset" would also work, yes.