tapeball calculations

TECHNICAL NOTE

What I won’t be doing is installing and photographing all the possible configurations of the nine tape balls.

Here’s why…

nine objects can be sequenced in 9! (factorial) ways

that’s 9*8*7*6*5*4*3*2*1 = 362,880

362,880 unique sequences

however

as we have three red, three grey and three white balls

that’s 3! * 3! * 3! = 216

reducing our unique sequences to just

9! / (3! * 3! * 3!) = 362,880 / 216 = 1,680

1,680 unique sequences

now 1,680 is a whole lot smaller than 362,880

but I am still not going to install and make you view 1680 photographs

at least not as static images!

I think this will be a task for an animation (maybe)…

PS. if I were to then look for rotations, reflections and rotation reflections, the 1680 unique sequences would become a smaller number of unique 3 x 3 grids, but I’ll save that for another day!

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