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<DIV><FONT face=Arial size=2>How many of you remember a game called Avalanche?
You can find a picture at</FONT></DIV>
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size=2>http://www.boardgamegeek.com/image/110686</FONT></DIV>
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<DIV><FONT face=Arial size=2>If you never played the game, I hope you get the
idea about how it works by looking at the picture.</FONT></DIV>
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<DIV><FONT face=Arial size=2>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.</FONT></DIV>
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<DIV><FONT face=Arial size=2>Let the hole be in row 0, and each successive row
of gates be row 1, 2, 3, ...</FONT></DIV>
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<DIV><FONT face=Arial size=2>After the nth drop, the first marble dropped is in
which row?</FONT></DIV>
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<DIV><FONT face=Arial size=2>After the nth drop, the nth marble dropped is in
which row?</FONT></DIV>
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<DIV><FONT face=Arial size=2>After the nth drop, the deepest marble is in which
row?</FONT></DIV>
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size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>On the nth drop, how many marbles
fall?</FONT></DIV>
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<DIV><FONT face=Arial size=2>On the nth drop, what is the total number of rows
fallen by all marbles</FONT><FONT face=Arial size=2>?</FONT></DIV>
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