Question: I've decided to relabel my clock in base 2. I will use the binary form of the numbers 1--12, I will arrange the twelve binary

I've decided to relabel my clock in base 2. I will use the binary form of the numbers 1--12, I will arrange the twelve binary numbers around the clock so that all of the numbers with a single 1 are next to each other, all of the numbers with two 1s are next to each other, and all of the numbers with three 1s are next to each other. In other words, there are three blocks around the perimeter of the clock, each consisting of binary numbers with the same number of 1s. How many circular arrangements of this type are possible?

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