REAL math stumper

[TuxDave]

Originally posted by: desteffy

Originally posted by: TuxDave


Yeah you got it. It was the only creative problem I saw using the pidgeon hole principle. What are you asking. If the plane was colored 3 different colors prove that 2 points 1 mile apart will be the same color?

yes

Given a plane RxR, color each point with one of three colors. Is it necessairly true that there will be two points exactly one mile apart of the same color.

ahh... goddammit. I'm guessing the answer is yes but I can't figure out which shape is easiest to prove it. So far I have two back-to-back equilateral triangles and the next was just a grid of dots. :-(

 

[desteffy]

Originally posted by: TuxDave

Originally posted by: desteffy

Originally posted by: TuxDave


Yeah you got it. It was the only creative problem I saw using the pidgeon hole principle. What are you asking. If the plane was colored 3 different colors prove that 2 points 1 mile apart will be the same color?

yes

Given a plane RxR, color each point with one of three colors. Is it necessairly true that there will be two points exactly one mile apart of the same color.

ah.. urr... gimme a sec.

hehe get out a pencil and paper, it took me one to remember the right picture

 

[TuxDave]

Originally posted by: TuxDave

Originally posted by: desteffy

Originally posted by: TuxDave


Yeah you got it. It was the only creative problem I saw using the pidgeon hole principle. What are you asking. If the plane was colored 3 different colors prove that 2 points 1 mile apart will be the same color?

yes

Given a plane RxR, color each point with one of three colors. Is it necessairly true that there will be two points exactly one mile apart of the same color.

ahh... goddammit. I'm guessing the answer is yes but I can't figure out which shape is easiest to prove it. So far I have two back-to-back equilateral triangles and the next was just a grid of dots. :-(

ok ok ok ok... I think I have a way with my triangle pair. The structure is pretty much static.

.1
23
.1

And in order to have no 2 colors 1 mile apart, this structure has to exist everywhere. However if you pivot the structure around one of the '1s' (because you need to fix one of the 1's to make the structure deterministic excluding the 2s and 3s), then the other 1 will eventually be 1 mile apart from the its original location. QED? lol! I think this is the nicest way I can put it. I tried shifting and sliding it all around and shrinking/enlarging it. What a mess.

 

[desteffy]

Originally posted by: TuxDave

Originally posted by: TuxDave

Originally posted by: desteffy

Originally posted by: TuxDave


Yeah you got it. It was the only creative problem I saw using the pidgeon hole principle. What are you asking. If the plane was colored 3 different colors prove that 2 points 1 mile apart will be the same color?

yes

Given a plane RxR, color each point with one of three colors. Is it necessairly true that there will be two points exactly one mile apart of the same color.

ahh... goddammit. I'm guessing the answer is yes but I can't figure out which shape is easiest to prove it. So far I have two back-to-back equilateral triangles and the next was just a grid of dots. :-(

ok ok ok ok... I think I have a way with my triangle pair. The structure is pretty much static.

.1
23
.1

And in order to have no 2 colors 1 mile apart, this structure has to exist everywhere. However if you pivot the structure around one of the '1s' (because you need to fix one of the 1's to make the structure deterministic excluding the 2s and 3s), then the other 1 will eventually be 1 mile apart from the its original location. QED? lol! I think this is the nicest way I can put it. I tried shifting and sliding it all around and shrinking/enlarging it. What a mess.

WINNAR!

 

[chuckywang]

desteffy: What school did you take the putnam for? How'd you do?

 

[desteffy]

Oakland university in michigan. graduated last year, my scores were 1,22,10,30

you?

 

[chuckywang]

Duke University for me: don't remember my exact scores but they were all in the 10-20 range. I am going to take it this year, so hopefully I can do better.