## Problem 420

A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
Forum rules
As your posts will be visible to the general public you
are requested to be thoughtful in not posting anything
that might explicitly give away how to solve a particular problem.

This forum is NOT meant to discuss solution methods for a problem.

In particular don't post any code fragments or results.

Don't start begging others to give partial answers to problems

Don't ask for hints how to solve a problem

Don't start a new topic for a problem if there already exists one

Don't post any spoilers
jpatou
Posts: 9
Joined: Sat Mar 09, 2013 8:13 am

### Problem 420

I've got a problem for this one : I find F(50) = 6 with these matrix
[5, 4]
[4, 5]

[10, 6]
[6, 10]

[17, 8]
[8, 17]

[20, 8]
[32, 20]

[20, 32]
8, 20]

[20, 16]
[16, 20]

Can someone check if these are correct and if so, which one I missed ?
Thanks

Ted
Posts: 19
Joined: Sun Apr 02, 2006 9:46 pm

### Re: Problem 420

These look correct.
The trace of the missing one is 26.
Good luck!

jpatou
Posts: 9
Joined: Sat Mar 09, 2013 8:13 am

### Re: Problem 420

Thanks very much .
I identified and fixed the bug. My function to test matrix candidates now works.
Now I have to think how to eliminate quickly most of the candidates.

3uc1id
Posts: 3
Joined: Wed Mar 27, 2013 10:13 pm

### Re: Problem 420

I actually computed 8 different matrices for F(50)!! Which is a liar?

[5 4]
[4 5]

[10 6]
[6 10]

[13 12]
[12 13]

[17 8]
[8 17]

[12 8]
[24 28]

[20 8]
[32 20]

[20 16]
[16 20]

[18 9]
[18 27]

RobA
Posts: 7
Joined: Sat Mar 23, 2013 11:00 pm

### Re: Problem 420

This same list of eight matrices is given in a math.stackexchange post http://math.stackexchange.com/questions ... -euler-420. That post also gives the square roots and those square roots are not all positive integer matrices.

3uc1id
Posts: 3
Joined: Wed Mar 27, 2013 10:13 pm

### Re: Problem 420

yeah, that post was me :p i didn't realize that 0 wasn't positive

3uc1id
Posts: 3
Joined: Wed Mar 27, 2013 10:13 pm

### Re: Problem 420

Does the answer to this fit in a C unsigned long int?

TheEvil
Posts: 84
Joined: Sun Nov 13, 2011 10:38 am
Location: Szeged, Hungary

### Re: Problem 420

Yes.

Jochen_P
Posts: 53
Joined: Mon Oct 05, 2009 9:47 am
Location: Stuttgart, Germany

### Re: Problem 420

I don't get this at all.. Can someone explain to me how these matrices relate to each other?
The sum of those matrices are different and I just can't make out any other relation

taking the sample:

Maybe I'm just a bit undercaffeinated?

hk
Posts: 10422
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: Problem 420

Squaring a matrix has nothing to do with matrix addition.
What you can read there is that for some matrices A,B,C holds that $A=B^2$ but also $A=C^2$

Jochen_P
Posts: 53
Joined: Mon Oct 05, 2009 9:47 am
Location: Stuttgart, Germany

### Re: Problem 420

Nope, sorry.
Still don't get it. Seems that I'm a bit thick today

 The only thing I see there is that the ratios on the diagonals are the same in every matrix, but how that accounts for those lesser matrices to be squared? No clue[/edit]

[edit 2] Animus was so kind to link me to the corresponding wiki article, Thanks [/edit]

RobertStanforth