Heck, you could have at least shown how to do Bingo in N dimensions! Or fractal dimensions... That's what really distinguishes mathematicians from engineers... At 02:03 AM 11/22/02 -0500, Ken Roberts wrote:
Hi Everyone,
Drifting a bit in topic header - about Bingo cards...
About 11 years ago a printing company hired me to help them develop some Bingo card "perms" (permutations) as they are called. Those are selections of numbers which can then be fed thru the printing process to produce cards. Some people with a mathematical bent make some of their income via the design of Bingo perms.
I've never played Bingo but understand that there are special games - normal Bingo is 5 in a row, then there is a need-both-diagonals variant, a large C variant (need top and bottom rows and left column), and large box variant (top and bottom, and left and right).
Bingo cards are often printed in triplets, that is three cards which use all 75 numbers. As you know col B has numbers 1-15, col I has 16-30 etc. It is considered "bad" to have all evens or all odds in a row or column, so you have fewer choices for each. It is also considered "good" for distinct cards in a perm to differ by at least 4 numbers from one another. There are not really septillions which are sufficiently different from one another to be acceptable for use in a Bingo parlour.
There's more but that may give you the flavour of the production of actual Bingo cards.
I didn't stay with the assignment very long. The math ran ahead of the programming. I showed that one of their desires, for a perm which was maximal in a certain sense, could not be achieved - and so they decided that their existing ad hoc perms from random generate-test-discard programs were maybe not so bad after all!
Actually, I didn't have to "show" anything except to myself. A simple statement, in a definitive tone of voice, that such and such had been proved to be impossible was sufficient to satisfy the client. A three sentence execution of the golden goose.
Bottom line: If you want to be a mathemagician, add some fuzz and mystery to your pronouncements.
Ken R.