Hexagons, permutations, and becoming a good swapper

I started the day by counting the number of African Flower hexagon motifs I needed to complete in order to be current with my swapping obligations.

I looked over my missed commitments for August, September, October, and November, and found that it would take 19 hexagons for me to be up-to-date, so I set out to make the five hexagons I was shy of the nineteen needed, and got them done before dinner.

Here they are:

Five African Flower hexagons posing for the camera
The same five hexagons in a more candid photo

Having crocheted myself out of swap arrears, I then turned my attention to a project that was completely driven by my desire to incorporate math with crochet.

In another time, in another place, I was a middle school math teacher. Part of the North Carolina math curriculum for 7th graders at that time involved combinations and permutations.

I had made the Babette inspired squares with two things in mind. First, I wanted to make a series of 3-round squares with each square composed of 2 colors (r). Next, I selected 8 colors (n) that I thought worked no matter how they were paired. Then, it was a simple matter of calculating the number of squares I would need to make by taking my n (the total number of colors) and my r (the total number of colors used per square) and plugging them into this handy formula: n!/(n-r)!

The result was 56. (If you want to check my work, here is a handy combination and permutation calculator).

I reviewed my permutation squares (as I have come to think of them) in the light of day.

Thirty-six of the 56 permutation squares

While I am not entirely certain of what these square will become, I am leaning toward making two of each permutation for a total of 112 squares and arranging them in a rectangle that is either 7×16 squares or 8×14 squares which will then serve as a cat runner on the top of my sofa.

In the meantime, I have some envelopes I need to address so I can send the African Flower hexagons to their rightful owners.

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2 thoughts on “Hexagons, permutations, and becoming a good swapper

    1. It is the Red Heart Super Saver colors pumpkin and maize. It is one of my favorite combinations.

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