[eastbay]

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So I might have miscounted something but that gives me:

28,626 + 6,097 + 54,756 = 89,479 such hands.

But it is late so I may have miscounted.

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I got 83,473. I found my answer via an equivalence class generating algorithm (because I wanted my method to be general for the N-way problem), so it's hard to tell where the discrepancy might be. Pretty close, though.

eastbay