Pedro has a collection of 100 rocks. At the beginning of each day, he collects all the rocks into a single collection. Then he then divides the rocks into two smaller collections, one with a rocks and one with b rocks (so a+b= 100), and he writes down ab (the product of their sizes) on a card. Then he goes to one of the his two collections and divides it into two smaller collections, one with c rocks and one with d rocks, and writes down the product cd of their sizes on the card. So now Pedro has three collections. He now goes to one of the collections and divides it into two smaller collections of sizes e and ƒ and writes ef on the card. He continues in this way until he is forced to stop because he has 100 collections with 1 rock each. At this point he has written down 99 numbers on his card. He adds up the numbers and calls this number the score for the day. Pedro repeats this experiment each day, but can make different decisions about how to divide collec- tions. For example, maybe on the first day he divides the collection of 100 rocks into collections of 57 and 43, and then divides the collection of 57 into 4 and 53, and so forth. But maybe on the second day he divides the collection of 100 into collections of 50 and 50, and then divides one of the collections of 50 into 22 and 28, and so forth. Pedro is interested in making his score for the day as large as possible, and on the seventh day, he achieves this. What is his score on the seventh day?
Pedro has a collection of 100 rocks. At the beginning of each day, he collects all the rocks into a single collection. Then he then divides the rocks into two smaller collections, one with a rocks and one with b rocks (so a+b= 100), and he writes down ab (the product of their sizes) on a card. Then he goes to one of the his two collections and divides it into two smaller collections, one with c rocks and one with d rocks, and writes down the product cd of their sizes on the card. So now Pedro has three collections. He now goes to one of the collections and divides it into two smaller collections of sizes e and ƒ and writes ef on the card. He continues in this way until he is forced to stop because he has 100 collections with 1 rock each. At this point he has written down 99 numbers on his card. He adds up the numbers and calls this number the score for the day.
Pedro repeats this experiment each day, but can make different decisions about how to divide collec- tions. For example, maybe on the first day he divides the collection of 100 rocks into collections of 57 and 43, and then divides the collection of 57 into 4 and 53, and so forth. But maybe on the second day he divides the collection of 100 into collections of 50 and 50, and then divides one of the collections of 50 into 22 and 28, and so forth.
Pedro is interested in making his score for the day as large as possible, and on the seventh day, he achieves this. What is his score on the seventh day?
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