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A previous question asked whether the map of the USA needs four colors.

Now, what about Canada? If you want to assign a colour to each province and territory, so that no two neighbours have the same colour, do you need four different colours?

When I was a young man, I knew the answer to that question. But then, when I was half as old as I am now, I found I did not know the answer anymore!

How old am I? At what point did I get confused?

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You are

42 years old

You became confused

exactly 21 years ago on April 1, 1999 when Nunavut became a territory.

Your confusion may have been due to this

In the legal definition of Nunavut, its border is specified as "Commencing at the intersection of 60° 00' N latitude with 102° 00' W longitude, being the intersection of the Manitoba, Northwest Territories and Saskatchewan borders". Since the intersection does not lie exactly at those coordinates, the laws are not perfectly clear about whether or not the Nunavut-Northwest Territories boundary, which has not been completely surveyed, is to meet the others in a quadripoint.

If they don't

meet in a quadripoint, a fourth color might be needed.

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  • $\begingroup$ Exactly! But perhaps you could explain why that confused me. $\endgroup$ – deep thought Apr 1 at 4:20
  • $\begingroup$ @deep thought Suggestion made. $\endgroup$ – Jens Apr 1 at 4:57
  • $\begingroup$ The last sentence sounds incorrect to me. Are you missing a negative somewhere? $\endgroup$ – deep thought Apr 2 at 1:51
  • $\begingroup$ @deep thought No, I don't think so. Areas which only share a single point don't need different colors. In the map coloring world, they don't have a common border. $\endgroup$ – Jens Apr 2 at 3:32
  • $\begingroup$ Well ... setting that aside, the last sentence sounds like it is saying the converse -- if they don't share a common point, they do need four colours -- and that doesn't sound right. $\endgroup$ – deep thought Apr 2 at 4:06
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Extending @Jens' answer:

Nunavut, NorthWest Territories, Saskatchewan and Manitoba all share a common point in their boundaries. This planar map therefore needs four colours, although the common point can only belong to one of the regions, and so your confusion is that are the four territories actually neighbours, or will three colours still suffice.

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    $\begingroup$ As I understand it, areas that only share a single point don't need to have different colors. This shouldn't have confused. $\endgroup$ – Jens Apr 1 at 4:50
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    $\begingroup$ @Jens is right. If territories sharing a single point would need all different colors, then one could easily build a map which would need more than 100 colors. $\endgroup$ – Falco Apr 1 at 14:44
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    $\begingroup$ Exactly @JMP. This is the point at which I became confused. $\endgroup$ – deep thought Apr 2 at 1:25

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