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An Analysis Of Peg's Collapse

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Peg was going to the market when she hit a pothole and all of her eggs broke. Unfortunately Peg was not hurt. Peg had put the eggs into groups of two,three,four,five, and six. In the groups she always had one extra egg left over. When she put it into a group of seven she did not have any eggs left over. After Peg hit the pothole she wanted her insurance company to pay some money for the eggs that were broke. Her insurance agent asked her how many eggs she had fortunately she did not know. I started out by listing every multiple of seven up to two hundred which are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203. I can cross off every multiple of 2 because if I

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