HSC 2013 MX2 Marathon (archive) (4 Viewers)

Status
Not open for further replies.

braintic

Well-Known Member
Joined
Jan 20, 2011
Messages
2,137
Gender
Undisclosed
HSC
N/A
Re: HSC 2014 4U Marathon

Consider a regular 8x8 chessboard. 8 knights are placed on the chessboard, 4 at each end as such:

_ _ K K K K _ _

So in the middle of the very top and very bottom rows is 4 knights.

If all knights move simultaneously, prove whether or not it is possible for either of the diagonals of the chessboard to be completely filled by all 8 knights.
After how many moves? As many as you need?
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: HSC 2014 4U Marathon

Nope, there will always be four knights on dark squares and four knights on light squares (as this is the case to start with, and each move changes the colour of each knights square).
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon

Ok yer you do the same thing and you get c>d too.

Then you will probably do something similar and get all the results.
 

dunjaaa

Active Member
Joined
Oct 10, 2012
Messages
473
Gender
Male
HSC
2014
Re: HSC 2014 4U Marathon

Do we learn these inequality results later when we cover harder 3U?
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: HSC 2014 4U Marathon



Note: This question should probably be split into several parts in order to make the difficulty more reasonable, but I would like to see what you guys can come up with off the bat.
 
Last edited:

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon



Note: This question should probably be split into several parts in order to make the difficulty more reasonable, but I would like to see what you guys can come up with off the bat.








As then the RHS as

What am I doing wrong?

If this is actually correct then I'm going to try find an upper bound for then call on my best friend Mr.Squeeze Theorem.
 
Last edited:
Joined
Sep 20, 2010
Messages
2,225
Gender
Undisclosed
HSC
2012
Re: HSC 2014 4U Marathon

It should be



on the second last line
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: HSC 2014 4U Marathon









As then the RHS as

What am I doing wrong?

If this is actually correct then I'm going to try find an upper bound for then call on my best friend Mr.Squeeze Theorem.
Whoops, my bad, I forgot to include a factor inside the brackets. You need to average the power sum before taking the p-th root. Edited appropriately.
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon

Whoops, my bad, I forgot to include a factor inside the brackets. You need to average the power sum before taking the p-th root. Edited appropriately.
Ok so that gives me my lower bound:



Now I need to find an upper bound to use Squeeze Theorem on (well at least that is what I'm thinking will happen).
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 4)

Top