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Bingo Cards
Taking the uppermost corner square in Column B of a bingo card, there are 15 possible numbers; from 1 to 15. The number in the next square down in the column also has to be 1 to 15, but cannot duplicate the first number, so there are 14 possibilities. Using this logic and continuing to the bottom of the column, there would be 13, 12 and 11 possibilities in each of the remaining squares in the column.
Given this, the number of possibilities existing just in Column B alone would be 15 x 14 x 13 x 12 x 11, or 360,360.
Columns I, G and O would duplicate this data.
Column N, due to the Free Spot square, would have only four squares to fill, but the logic remains the same. Therefore, the number of possibilities in this column would be 15 x 14 x 13 x 12 or 32,760.
Given this, the number of different bingo cards possible is 360,360 x 360,360 x 360,360 x 360,360 x 32,760 or 552,446,474,061,128,648,601,600,000.
Mathematical formulas:
Columns B, I, G and O - (15!/10!) = 360,360
Column N - (15!/11!) = 32,760
Card - ((15!/10!)4 x (15!/11!))=552,446,474,061,128,648,601,600,000.
Another way of calculation would be:
In each of the five squares in the first row of the card there are 15 possibilities each.
Given this, the alternate formula for the total number of possibilities is:
155 x 145 x 135 x 125 x 114 or (15 x 14 x 13 x 12)5 x 114 = 552,446,474,061,128,648,601,600,000.
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There are 24 different numbers on each bingo card. The number of cards with the exact same numbers in a different order can be calculated as (5!)4 x (4!) = 4,976,640,000.
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I have yet to find the number of cards possible with a distinct number combination differing from that of any other card in the group. Legend has it that a mathematics professor at Columbia University, Carl Leffler, detailed 6,000 different cards before he went insane.
Links
Given this information, it is doubtful that anyone would ever attempt to publish a web site, a book, or anything anywhere listing every possible bingo card combination. Just a chart in its simplest form such as what I've started would occupy an astronomical amount of disk storage space. However, a view of the very start of this can be found on the links below.
Individual bingo cards displayed in tables.
Bingo card chart 01.
Bingo card chart 02. Not currently posted - available on request.
Bingo card chart 03. Not currently posted - available on request.
Bingo card chart 04. Not currently posted - available on request.
Bingo card chart 05. Not currently posted - available on request.
Bingo card chart 06. Not currently posted - available on request.
Bingo card chart 07. Not currently posted - available on request.
Bingo card chart 08. Not currently posted - available on request.
Bingo card chart 09. Not currently posted - available on request.
Bingo card chart 10. Not currently posted - available on request.
Bingo card chart 11. Not currently posted - available on request.
Bingo card chart 12. Not currently posted - available on request.
Bingo card chart 13. Not currently posted - available on request.
Bingo card chart 14. Not currently posted - available on request.
Bingo card chart 15.
Bingo cards with the same numbers in different order.
If viewed, note that all the numerical changes occur in Column O only. I have no intention of progressing beyond there, and might not even complete the development of the charts and tables to that point. The charts and tables were designed to be viewed and the cards numbered in numerical order, from lowest to highest.
This table will be used as a tool for the development of a sequential card numbering system. The first phase may seem simple in appearance, but subsequent tables will utilize multiples of the numbers currently displayed. It is a long-term project.
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=^.^=