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Nein, Nine!

Suppose that, after going through a town gate, you see 9 dykes, with 9 trees on each dyke, 9 branches on each tree, 9 nests on each branch, and 9 birds in each nest, where each bird has 9 fledglings and each fledgling has 9 feathers with 9 different colours in each feather. How many are there of each?


Source: Problem in Sun Zi's Mathematical Manual, circa 500