Circle Coloring

Algebra Level 1

Gabe gave Rin this circle, after he divided it into 10 parts. Then, he asked her if she can color 9 of the parts under these conditions:

1) Use 3 different colors

2) Two parts that are the same color can't touch each other

Can Rin color the circle under these conditions?

Yes, she can No, that's impossible

Christine Katsamatsa by Christine Katsamatsa , 16, Greece

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2 solutions

Blan Morrison
Sep 15, 2018

Here is an example:

15 Helpful 1 Interesting 0 Brilliant 0 Confused

That is the only solution for coloring all 10 parts.

Steve Brian - 2 years, 8 months ago

Wait. shouldn't either the top or bottom red part be white??

Sam Leong - 2 years, 8 months ago

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What do you mean?

Blan Morrison - 2 years, 8 months ago

Only 9 parts were asked to be coloured!

Manya Singh - 2 years, 8 months ago

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Yes, but this is a proof for 10. Therefore, it can be done with 9.

Blan Morrison - 2 years, 8 months ago
Jeremy Galvagni
Sep 17, 2018

I'm not sure of the full rule for when a map can be 3-colored. Part of it must have to do with regions that are completely surrounded by other regions. If any of these are surrounded by an odd number of regions (>1) then it definitely cannot be 3-colored. In this map, the two central regions are each surrounded by 6 others which is a good sign.

It turns out to be a pretty easy task. You can see @Blan Morrison 's solution.

2 Helpful 1 Interesting 0 Brilliant 0 Confused

I know that the 2 central regions are each surrounded by other 6 regions. I did that by prupose. It is meant to be an easy task.

Christine Katsamatsa - 2 years, 8 months ago

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