Presents to Self (Solitaire IV)

A birthday in quarantine is a limited experience.

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Above is the 2020 Glenburn Moonshine Elite, the only Darjeeling that has made it to me this year so far. An amazing tea.

Below are some Pu-Erh cakes that will hopefully last a year.

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More food, for heart and brain:

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Of course there needs to be a puzzle. Let’s call it Quarantine. You have to go on an errand, visiting all twenty vertices of the map below (it will take a while to walk this, I hope).Errands 01

But there is a curfew. This means that you can only visit each of the twenty places once. If you are seen somewhere a second time, you become suspicious and will be eaten by a grue. You also need to end up where you started — sleeping in someone else’s home is suspicious.

Finally, traveling from place to place requires a special permit in the color of the edge along which you travel. So you will need to carry a few permits (being eaten by a grue is unpleasant). For instance, an orange permit will allow you to use any of the orange edges as often as you dare, but only those. There are six different colors, and hence six different permits.

Permits are expensive. What is the smallest number of permits that allows you to visit each place exactly once, returning to your starting point at the end?


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