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 Question from Martin: I'm trying to produce bingo cards. There are only 4 numbers on each bingo card. The numbers are between 1 and 12. How do i produce as many bingo cards as possible without duplicating number combinations? Thanks

Hi Martin,

There are "12 choose 4" = 12x11x10x9/(4x3x2x1) = 11x9x5 = 495 different combinations of 4 numbers chosen from {1, 2, ..., 12}. You can generate all of these by listing them in the same order as they'd appear in the dictionary:

1,2,3,4
1,2,3,5
...
1,2,3,12
1,2,4,5
1,2,4,6
...
1,2,4,12
1,2,5,6
...
1,3,4,5
etc

The numbers in each list appear in increasing order. When a digit has reached its maximum possible value (12 for the last digit, 11 for the one before it and 10 for the one before that) the digit to its left is increased by 1 and then each subsequent digit to the right is one more then the one to its left. For example, the element of the list that follows 3, 5, 11, 12 is 3, 6, 7, 8.

If the position of the numbers on the cards also matters, then it is possible to make more than 495 cards. Each collection of 4 numbers can be used to make 12 cards if any number can appear in any position, and can be used to make 6 cards if all that matters is what column a number is in.

Victoria

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