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1/25-1/31 POTW

Seven balls are numbered 1 through 7. There are three buckets; one red, one green, and one blue. How many ways are there to put them into the buckets such that no two consecutively numbered balls go into the red and green buckets, no three consecutively numbered balls go into the blue bucket (but two consecutively numbered balls can), and the blue bucket can't be empty?

No two consecutive numbers can both be placed in red, and no two consecutive numbers can both be placed in green (i.e., 1,2 both red is not allowed, but 1 red and 2 green is allowed).

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Written by Elaine Zhou​

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