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In front of you sits a pile of n stones. You split the pile into...

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In front of you sits a pile of n stones. You split the pile into two smaller piles, count the number of stones in the smaller pile, j, and write down the number 21. Then, for each of the two piles, you split them and write down their versions of 21. You repeat this process, splitting piles and writing down exponentials until all piles have only 1 stone in them. Fi- nally, you multiply together all the numbers you wrote down. For example, if we start with 8 stones, one possible way these piles could be split is as follows: 8 5 2^3=8 3 2 21=2 2^2=4 3 2 211= 241=2 2 1 2^1=2 1 241=2 1 Product = 8*4*2*2*2*2*2 = 1024 818 = 16,777,216 1024

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