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# Treebeard's Stumper AnswerSeptember 26, 1997

Here's another stumper involving eggs, but not really about eggs. A farmer is taking her eggs to market, trying to pack them neatly for sale. She notices that if she packs them in groups of two, three, four, five, or six, there is always one egg left over. But if she packs them in groups of seven, they are all in complete groups with no eggs left over. So how many eggs does she have? There's more than one answer, so find the smallest. What do they all have in common? Hint: think about factors and remainders!

In groups of 2, 3, 4, 5, or 6, there is always one egg left over. Many people figured that there must be 61 eggs. But an important line was inadvertently left out of the Newsnote, that there are no eggs left over in groups of 7, and that's harder. Knowing that the answer must be a multiple of 7, I used brute force to get the answer of 301 eggs. There are other solutions since you can add any multiple of 3 x 4 x 5 x 7 = 420 (the least common multiple) to get another one. It's interesting how hard it is to attack this problem with remainders!

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