Mind Blogging- Blingo

posted Tuesday, 3 January 2006
Er.

I mean mind boggling bingo.

In the game of BINGO there are seventy-five numbers broken up into five groups of fifteen numbers each; B-1 thru 15, I-16 thru 30, N-31 thru 45, G-46 thru 60, and O-61 thru 75.
The BINGO card has five columns corresponding to the letters B-I-N-G-O. The player's card has twenty four numbers; five numbers pre-printed in four of the columns under the B-I-G-O and four numbers under the N.

Calculating the total number of possible combinations yields the result that there exists
552,446,474,061,129,000,000,000,000. (That's 552-million-billion-billion or 0.5 quadrillion) possible BINGO cards.
There would be 111,007,923,832,371,000 sets of cards with 4,976,640,000 cards (almost 5 5 billion) in each set. Every card in each set would have the same twenty four numbers, but in a different arrangement on each card.

If we presume that there are six billion people in the world today, that means that there are 92,074,412,343,521,400 cards for each and every person in the world.

Doesn't it make you wonder how the BINGO Barons choose which cards to print?
If you could print a million cards per second, it would take
17,505,972,382,599.7 years to print every possible BINGO card.

If you put four BINGO cards on a standard 8-1/2 X 11 sheet of paper, and if you spread all of the BINGO cards out over the surface of the earth, they would cover the earth to a depth of over 800 miles.

If there were one million cards per inch of height, and all of the possible cards were put in one stack, the stack would extend for 1485 light-years. (A light year is 6-trillion miles.)
Alpha Centuri, our nearest star beyond the Sun, is only 4 light-years away.

Here's some proof. You can have 120 different arrangements of five numbers under each of the four columns under the B, I, G, and O. You can have 24 different arrangements of the four numbers under the N. So, 120 times, 120 times, times 24, times 120, times 120 equals 4,976,640,000. That's the number of cards that could exist, all with the same twenty-four numbers, but just in a different arrangement on each card.


Doing the arithmetic then, there are 111,007,923,832,371,000 possible unique BINGO combinations where no two cards would have the same twenty four numbers. (That's 111-million-million.)

		Possible Combinations	Possible Combinations
Numbers Covered	Numbers Uncovered	Including Free Space	Neglecting Free Space
0	24	1
1	23	24	23
2	22	276	253
3	21	2,024	1,771
4	20	10,626	8,855
5	19	42,504	33,649
6	18	134,596	100,947
7	17	346,104	245,157
8	16	735,471	490,314
9	15	1,307,504	817,190
10	14	1,961,256	1,144,066
11	13	2,496,144	1,352,078
12	12	2,704,156	1,352,078
13	11	2,496,144	1,144,066
14	10	1,961,256	817,190
15	9	1,307,504	490,314
16	8	735,471	245,157
17	7	346,104	100,947
18	6	134,596	33,649
19	5	42,504	8,855
20	4	10,626	1,771
21	3	2,024	253
22	2	276	23
23	1	24	1
24	0	1
Total		16,777,216	8,388,607

Isnt that amazing? Doesnt it bloggle your blind?Uh, boggle your mind?