Upgrade 7 - 2 + 2 + 9 = 13 2 * 3 * 6 = 36 2 + 3 + 6 = 11 3...

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Josue G. Roman CS301K Dr. Cathy Stacy Nov. 02, 2006 “Upgrade 7” The Mathematician’s Children Guiseppe was a very intelligent mathematician who once asked his older mathematician friend Richard the ages of his three children. The following conversation ensued: Richard: The produce of their ages is 36. Guiseppe: That doesn’t tell me their ages. Richard: Well, by coincidence, the sum of their ages is your own age. Guiseppe (after several minutes of thought): I still don’t have enough information. Richard: Well, if this will help, my son is more than a year older than both of his sisters. Guiseppe: Oh good! Now I know their ages. What are their ages? (You may assume that Guiseppe knows his own age.) Solution The following are the only triples whose product is 36, and their sums. 1 * 1 * 36 = 36 1 + 1 + 36 = 38 1 * 2 * 18 = 36 1 + 2 + 18 = 21 1 * 3 * 12 = 36 1 + 3 + 12 = 16 1 * 4 * 9 = 36 1 + 4 + 9 = 14 1 * 6 * 6 = 36 1 + 6 + 6 = 13 2 * 2 * 9 = 36
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Unformatted text preview: 2 + 2 + 9 = 13 2 * 3 * 6 = 36 2 + 3 + 6 = 11 3 * 4 * 3 = 36 3 + 4 +3 = 10 It can be easily tell that Guiseppe is 13 years old, because when he was told the product of their ages was 36 he only had those 8 possible triplet combinations. The he was told the sum of their ages was his own age. Since we assumed he knows his own age, and even knowing that information he couldnt guess the ages, the only sum that is repeated is 13, that means it appears twice so he couldnt figure out which one was the correct triplet. Guiseppe knew the triple was either 1,6,6 or 2,2,9, but he had no way of telling which. Then hes told that the son was at least one year older than both of two daughters, leaving the triplet 1,6,6, out simply because one is not greater than 6. . So then he knew that 2,2,9 was the correct triplet, and that the son must be 9 years old and his two sisters are both 2 years old....
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