Wikipedia:Reference desk/Archives/Mathematics/2012 August 6

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August 6

Bingo (U.S. & Canada) Question

Assume you are playing bingo by typical U.S. rules, with cards as described here. All of the game's participants start the game with only one covered square, the "free space" in the center. The numbers 1-75 are then randomly drawn, one at a time. No number can be drawn twice. Once one player covers up five squares in a row on his card, he will have "Bingo", and the game will be over. What is the maximum number of numbers that can be drawn without any one player having Bingo? MMS2013 18:51, 6 August 2012 (UTC)

Let's see, you can have only 5 blanks and still not have a bingo, like so (there are 24 such configurations):

  x x x x
x x x   x
x x x x     
x x   x x
x   x x x

(I can list the other 23 configurations if you want.) If every player has cards set up so those same 5 numbers will block all bingos, it's theoretically possible (though a practical impossibility) to draw 70 numbers before somebody gets a bingo. StuRat (talk) 19:55, 6 August 2012 (UTC)