Problem 180

[ed_r]

Does n have to be a positive integer?

For example, is this a valid solution: x=[frac]1,2[/frac], y=[frac]1,3[/frac], z=[frac]1,5[/frac], n=-1 ?

 

[Robert_Gerbicz]

Yes, n can be negative value!

And don't forget the crazy problem statement: "the sum of all distinct s(x,y,z)" so if another triplet gives you the same s(x,y,z)=x+y+z value
then add only once.

[ed_r]

*Groan* ... and here's me hoping I wouldn't have to treat the n<0 cases specially.

Summing all those s values for n<0 is going to be a challenge ...

Out of interest, dev team, what "Raymond score" did you tentatively assign to this one?

[hk]

Out of interest, dev team, what "Raymond score" did you tentatively assign to this one?

very tentatively: 5

to clarify:
1,2,3: easy
4,5,6: medium
7,8.9: hard

[ed_r]

Holy **** ! I'm doing something wrong, obviously. Will look again this evening when I've more time.

[arif]

Who is Raymond?

[daniel.is.fischer]

Raymond is rayfil, he had the idea to give the problems an estimated difficuty score, so we can better judge which problem to publish when. However, the solvers don't always conform to our estimate

[stijn263]

What about adding a poll to every (new) problems' forum asking solvers how difficult they'd rate the problem?

That should give developers a better understanding of what subjects are percieved to be difficult by the average PE user

[Oakenshield]

Hi everyone,

I thought that I had solved this difficult and beautiful problem but it's not the case ! I was a bit disappointed and surpressed because my analyze is based on some powerful theorem...

I've made a lot of checks, I can't see what's wrong, I'm sure of my answer... I've found that with k=10 (and not 35), the solution would be 12519... Is this correct ? Can anyone give me a suggestion to find my error(s) ?

Thanks a lot !

[daniel.is.fischer]

Your value for k = 10 is correct. Can't say what your problem is without knowing what you do. Perhaps if you PMed me an outline of your approach, I could give a hint.

[axelbrz]

Hi, I have two questions:

1) if (a, b, c) is a golden triple of order k. (b, a, c) is a different golden triple, right? Or is it different?

Because f_n(a, b, c) = f_n(b, a, c) for all a, b, c, n,


2) Can n be zero or negative?

Thanks!

[jaap]

1. Would the answer to the problem be any different?
2. Yes.

[axelbrz]

Oh, sorry, you're right! s(x, y, z) = s(y, x, z) so it will be added once to t.

Thanks!

[DNS]

I have no more ideas. Can somebody give me a hint?
For k=10 I obtain the set with 71 different s(x,y,z) varied from 2/5 to 20/9, with total 23113/280.
I found a Great theorem (mentioned above), look through positive and negative n.
Where could be a mistake?

[daniel.is.fischer]

You are missing some values, there are 76 for k = 10. You could PM me your approach, maybe I can find a legitimate hint.

[DNS]

Thanks Daniel!
This hint was enough to locate a mistake.

[mantonetti]

I'm stuck at 71 solutions for the case k=10 (with u+v=23393) but from previous posts I see there are 76 solutions.

Is there someone who can give me a hint please?

[Steve N]

Well this is puzzling. I have some fast code that gives the right answer when k=10 (previous posters suggest that for k=10 there are 76 distinct values of s giving a final answer of 12519).

And yet for k=35 I am coming up short. I have been over my code backwards and forwards and can't think where it might be going wrong.

Would anyone be kind enough to offer a suggestion? What am I likely to be doing wrong?

[Steve N]

Is anyone able to confirm the number of distinct s values for k=35? I am reluctant to post my own figure here...

[Steve N]

Resolved the problem. Just needed to use "biginteger" in my fraction class instead of "long". I'm no programmer, so I'm still confused. Why didn't I get an overflow error if I was stretching my "long" variables too far?

Sorry to have bombarded this thread.