Project Euler Forum

Hi, I read the statement of Problem 452 (View Problem) and it states that F(10,10)=571. The way I interpreted the question I believe it is incorrect so I don't really know how I should interpret the question.

To calculate F(10,10) I would take all 10^10 combinations of a 10-tuple with numbers 1 to 10 and try if their product is less than or equal to 10. I made a bruteforce program for that and it gave me 391.
I also calculated it by hand and I got 391 too.

Can anyone clarify the problem statement since I probably didn't understand it in the correct way ?

gelatine1 wrote:...
To calculate F(10,10) I would take all 10^10 combinations of a 10-tuple with numbers 1 to 10 and try if their product is less than or equal to 10. I made a bruteforce program for that and it gave me 391. I also calculated it by hand and I got 391 too.
Can anyone clarify the problem statement since I probably didn't understand it in the correct way ?

Your interpretation seems correct, but you may have a counting mistake. Let's try smaller numbers:
F(1, 1) = 1
F(2, 2) = 3
F(3, 3) = 7
F(4, 4) = 19
F(5, 5) = 31
F(6, 6) = 76
F(7, 7) = 106
F(8, 8) = 253
F(9, 9) = 373
Can you get these?

oops I got a mistake for F(4,4) and I found the problem. I had made some wrong assumptions to simplify my program(since 10^10 cases would be too much) and I found my mistakes in my counting too.

thanks for the help

does order matter?
are (10,1,..) and (..1,10,1...) different solutions?

You can find out by trying both options for F(10,10).
Somewhat higher in this thread you can even find smaller cases to verify which of the two options holds.