Office Bingo

At work we are running a Bingo game for United Way charity in which we purchased 3 cards for about $5 and the winner splits the total collection in half with the charity.  Numbers are picked by a program and put on our corporate intranet site and I currently need 3 numbers for a full clear to win.

This got me thinking about the math and geometry behind Bingo cards.  For example, did you know that 5 blank numbers in a diagonal across the board is the minimum you need to block any full rows or columns? 

Did you know that even if the FREE middle square is counted as given, 5 is still the minumum number you need to block rows & columns, you simply blank out the number above FREE and to the left of FREE and give them the FREE and diagonal square in I column (or a similar mirror pattern)?

Or this, based on a choose formula of C(5, 15)xC(5, 15)xC(4, 15)xC(5, 15)xC(5,15) you have a total 111,007,923,832,370,565 possible winning card combinations. C(5, 15) is 3,003 possible combinations for a single column.

I was about to figure out my rough odds of winning based on the fact that 58/75 numbers have been drawn (find out the number drawn from each column and the number left in each column, etc) but when I started to think about it I realized I don't really care that much and I should probably do actual work today.  But heck it was fun thinking about it.

I also invented the concept of a Super Bingo that uses unique permutations instead of just combinations, meaning that 5 bingo cards with the exact same numbers would not all be winners at the same time.  So you would be drawing B-(3)-10, meaning Column B, Row 3, number 10.  This could work for World Bingo events where the number of possible participants warrants a greater number of possible combinations.

Now I know why all those old folks like bingo so much, they must be doing the math while they blot away!