Originally Posted by

**jonarmani** Ok Plato, I see how you got the 6 at least. In the attached image, I show a simplified version of the problem: A pool of 3 items in 5 slots. My drawing is all possibilities starting with item 1. The total number of possibilities would include a similar tree for sequences starting with 2, and then 3. The total number of sequences [paths through the tree] is equal to the number of nodes on the bottom row, which is 16 in this tree. Therefore, the total answer to this one is 3 * 16 = 48. Since my original puzzle involves 6 items, there will be 6 of these trees. That easily explains the 6 in your answer.

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