The new problem is for older students -- say 10th grade+? There is a pile of 20 stones. Joey divides it into two piles and writes down the product of their sizes. He then takes one of the remaining piles, divides it into two, multiplies stone counts and so on. He continues until all piles have exactly one stone. For example, he can go 11 + 9 leading to a product of 99, then split 11 = 3 + 8, leading to a product of 24, then split 9 = 6 + 3, giving a product of 18). In the end Joey computes the sum of all products, i.e. 99 + 24 + 18 + ... + 1. What is the largest value that this sum can attain? Prove your answer. Going back to last weeks question, there are three known solutions: The most common: 7 * 7 * 7 + 7 + 7 * 7 * 7 + 7 = 700 The second most common: 7 * 77 + 77 + 77 + 7 = 700 The least common: 7 * (7 * (7 + 7) + 7/7 + 7/7) = 700 Good luck!
Posted on: Tue, 19 Nov 2013 03:07:26 +0000
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