341Putnam 2009
Alan and Barbara play a game in which they take turns
filling entries of an initially empty 2008 × 2008 array.
Alan plays first. At each turn, a player chooses a real
number and places it in a vacant entry. The game ends
when all the entries are filled. Alan wins if the determinant
of the resulting matrix is nonzero; Barbara wins if
it is zero. Which player has a winning strategy?
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UP 0 DOWN 0 0 5
5 Answers
11A determinant is zer o if any two rows or colunms are equal
Therefore Barbara has a wining chance . She has to copy any one of the row or column numbers placed by alan
1its putnam 2008
putnam 2009 will be there on 5 dec 2009. its not yet conducted
1yes virang your solution is correct because
If Alan ever writes a number in one of the first two rows, Barbara
writes the same number in the other entry in the pair.
If Alan writes a number anywhere other than the first two
rows, Barbara does the same thing.
then as said by virang,
A determinant is zero if any two rows or colunms are equal