Like math problems? How about figuring out how many ways you can make change for $100. No worries, we have the answer

Like math problems? How about figuring out how many ways you can make change for $100. No worries, we have the answer

You know those people in school that always seem a bit too smart for their own good and have enough free time on their hands to put it to really silly uses? Well, get ready for a seriously mind-boggling math fun fact. There are 9,823,546,661,905 ways to break a $100 bill. So, how would you like your change?


Larry King brought up in a 2001 USA Today column that there were 293 ways to make change for one dollar, in currently minted denominations. This is including the one dollar coin that was popular years ago but has since fallen out of favor. Using a half dollar there are 50 combinations and 242 combinations without, getting the 293 grand total.


Warning: Math mumbo-jumbo incoming. To get the answer for any denomination you use trhe coefficient of x^100 in the reciprocal of the following: (1-x)(1-x^5)(1-x^10)(1-x^25)(1-x^50)(1-x^100). That's multiplying everything with every coin denomination (penny, nickel, dime, etc).


$2 bills were allowed and there was no distinguishing between a dollar bill and a dollar coin.


There is some dispute, however, since the dictionary states that "change" is "a number of coins or bills whose total value equals a single larger coin or bill." Therefore, $1 can't be change for $1, skewing the results a bit.


(Source)





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