Monday, March 12, 2007

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?

2 comments:

Trixies said...

lots of spare time huh?

doodlehead said...

not that much.