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Currently watching Suits with the family, and an interesting little puzzle came up in the show. In Season 1, episode 8, there is a situation with money laundering from one account to many smaller accounts.

So the set up is something like “transfer out 100 million”, and then you have some number of smaller accounts that sum to 100 million.

When Lewis brought this up in the show, and Mike had a stack of papers to go through to identify the smaller accounts that summed up to the larger account, my son pointed out it would be too difficult to go through all of the permutations to figure it out. The total number of permutations would be something like:

Where A is the total number of accounts to look over, and k is the max number of potential accounts the money was spread around. b(A choose k) is my cheeky text format for binomial coefficients.

So this will be a very large number. 10,000 choose 4 for example is 416 416 712 497 500 – over 416 trillion. You still need to add in b(10,000 choose 2) + b(10,000 choose 3) + ….. b(10,000 choose k). With even a small number of accounts, the number of potential combinations will be very large.

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