Coloring hexagons

Probability Level 1

Is it possible to paint all the small hexagons in this picture either blue, red or yellow, such that no hexagons of the same color share an edge or a vertex?

Yes No

3 solutions

Geoff Pilling
Dec 8, 2016

$\boxed{\text{Yes}}$ like this:

It should be specified that "The picture given is not colored".

qiang xiao - 4 years, 6 months ago

Good point... I've added some clarification... @Calvin Lin do you suppose we should remove those three colors to avoid the confusion?

Geoff Pilling - 4 years, 6 months ago

Ah ic what the concern is. Will remove the colors from the image.

Calvin Lin Staff - 4 years, 5 months ago

Instead of trying to color them all in, I just chose the smallest hexagon pattern from the center (cluster of 7) and used that as a small scale. If it works on the small version I assumed it would work on the full sized hexagon.

Morgan Smuczynski - 4 years, 5 months ago

DID IT SAME

anshu garg - 4 years, 5 months ago

How you created this diagram?

Munem Shahriar - 4 years ago

Its been a while, so I don't remember... :-/

Geoff Pilling - 4 years ago

Morgan Smuczynski
Dec 18, 2016

Instead of trying to color them all in, I just chose the smallest hexagon pattern from the center (cluster of 7) and used that as a small scale. If it works on the small version, I assumed it would work on the full sized hexagon.

Vikram Nadar
Dec 19, 2016

Its the application of four colour theorem

There are only 3 colors given to color with.

Elliott J - 4 years, 5 months ago

Can you elaborate further? The four color theorem tells us that 4 colors are sufficient. How do we know that 3 colors are sufficient?

Calvin Lin Staff - 4 years, 5 months ago

Coloring hexagons

3 solutions

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