Avanlanche

[David Wilson]

How many of you remember a game called Avalanche? You can find a picture at

http://www.boardgamegeek.com/image/110686

If you never played the game, I hope you get the idea about how it works by looking at the picture.

My question is, envision an infinitely deep Avalanche board with a single hole on top, initially set so that all the gates lean left and the first marble placed in the hole gets caught on the first gate it meets. Now put marbles into the hole one by one.

Let the hole be in row 0, and each successive row of gates be row 1, 2, 3, ...

After the nth drop, the first marble dropped is in which row?

After the nth drop, the nth marble dropped is in which row?

After the nth drop, the deepest marble is in which row?

On the nth drop, how many marbles fall?

On the nth drop, what is the total number of rows fallen by all marbles?

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