Non-Crochet Math Needed

Strictly hypothetically speaking, let’s say a … ahem… friend of mine has seven pairs of Converse All-Stars Chuck Taylor high-tops in different exceptionally bright colors.  Please do not judge at this point.

Let’s posit that this Chuck-obsessed person never wants to wear these beauties in mated pairs.  After all, orange on both feet might feel pedestrian. But in the interest of fairness, for state occasions and under extreme peer pressure, matching shoes would be considered as a last resort.

Photo courtesy of Alex Iannelli

Here’s the part where you help me… uh, I mean… this person crunch the numbers.  How many combinations are possible:

  • If the least restrictions are applied… any pairings
  • If the pairs are never matched
  • If you don’t count mirror image pairs (for example Pink left/Yellow right and Yellow left/Pink right are counted as one combination)

Please do not belittle my computational skills.    Where crochet is concerned I can usually wrap my brain around most number problems.  If the stitch repeat is 3.75 inches wide, how many repeats should be created in order to achieve garment sizes from XS to 3XL? What if there must be 2″ positive ease and no partial repeats? What if the number of repeats must be a multiple of 2?  A multiple of 4?  That I can do.

But I admit that I so suck at sneaker math it’s not funny and my head hurts. This Chuck problem keeps going round and round. Is there some elegant formula that gives me the magic number? Short of pulling out all seven pairs and lining them up and counting, I am totally confused here. Please, I need some sleep.