Araneae 2 (Solitaire XIII)

Last week I introduced the six balanced spiders which reappear below with a slightly improved design, and asked to use six of each kind to create a 6×6 spiderweb so that adjacent cards color match at the legs, and each row and column contains exactly one balanced spider of each kind.

Balanced

I got hooked on these little critters and wrote some code to hunt down solutions for me.

Balancedsol1

The solution above is perfect in the sense that also left and right (resp. top and bottom) edges match, so that we can get a toroidal spiderweb (or an infinite periodic one). There are still several hundred solutions. Not every possible first row can be extended to a perfect spiderweb, but the one below extends to a unique one. Can you find it?

Balancedprob2

There are other subsets of the 20 possible spiders that make nice puzzle sets. For instance the following are all possible spiders that have four different side patterns, i.e. one edge has to have green legs, another one pink, the remaining two mixed colors in different order. Let’s call them mixed spiders.

Totalspiders

We can again ask for perfect 6×6 spiderwebs, now using mixed spiders. In this case, there are only two different solutions. Below is the first row of one of them:

Totalprob1

I have no idea how hard it is to find the solution by hand. When I saw it, I was a bit upset. I will post it next week…

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