problem 452

[gelatine1]

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 ?

[mpiotte]

...
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?

[gelatine1]

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

[hamsterofdeath]

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

[hk]

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.