A pile starts with n sticks, with n>=2. The pile is split into two piles, and the product of the sizes of the piles is calculated. One of these new piles is then split into two piles, with the product of the sizes of these two new piles calculated and added to (the sum of) the previous product(s). This process continues until we have n piles with 1 stick in each.
For example, starting with 5 sticks, we could split 2, 3 (giving 6), then 2, 2, 1 (giving 6 + 2), then 1, 1, 2, 1 (giving 6 + 2 + 1), then 1, 1, 1, 1, 1 (giving 6 + 2 + 1 + 1 = 10).
Prove using strong induction that, no matter how the pile is split, the total at the end is always 1/2(n^2 -n).
Help?
2007-09-24
18:03:37
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2 answers
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Anonymous
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Mathematics