Er.
I mean mind boggling bingo.
In the game of BINGO there are seventyfive numbers broken up into five groups of fifteen numbers each; B1 thru 15, I16 thru 30, N31 thru 45, G46 thru 60, and O61 thru 75.
The BINGO card has five columns corresponding to the letters BINGO. The player's card has twenty four numbers; five numbers preprinted in four of the columns under the BIGO 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 552millionbillionbillion 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 81/2 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 lightyears. (A light year is 6trillion miles.)
Alpha Centuri, our nearest star beyond the Sun, is only 4 lightyears 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 twentyfour 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 111millionmillion.)

 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?
2 comments:
lots of spare time huh?
not that much.
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