Alice has a bucket of 900 pebbles. She wishes to pass them all to Bob.
Each stone must sit on a infinite checkerboard before Bob can take it.

Here are the rules:

1.      At most 36 pebbles can be on the board at any time.

2.      There are two types of moves:
        - Row move: Alice chooses a row of the board. She places as many
pebbles as desired (subject to rule 1) from her bucket to that row, in any
positions (but only one pebble per position).
        - Column move: Bob chooses any column of the board. He takes as
many pebbles as he likes from that column to his bucket.

3.      The game is over when Bob has all the pebbles, and the score is
the number of moves.

Alice and Bob are working together here, and their moves need not
alternate.

Can you find a strategy that allows the transfer of all the stones using
fewer than 300 moves?

How low can you go?

Source: Larry Carter,  Dept. of Computer Science, UC San Diego
(This is Macalester College Problem of the Week #871)

There will be a $1 prize for the best correct solution submitted by a
midshipman.

A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Thursday, October 22, 1998.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.

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Correct answers to problem #76 (stock-buying) came from Midn. 1/c Bussman
and Bunchongchuitr, 2/c Dickman and Kim, and 4/c Holmes, from MAJ
McCarthy, and from one midshipman's father.  Each of the explanations,
however, was incomplete.  Prize to Midn. Kim, whose solution is posted on
the bulletin board in the Chauvenet lab-deck corridor.