SOLUTION: Each of three players has written a list of 100 words. The lists are compared and all the words that appear in at least two lists are crossed out. Is it possible that 54 words rema

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Question 888260: Each of three players has written a list of 100 words. The lists are compared and all the words that appear in at least two lists are crossed out. Is it possible that 54 words remain in the first list, 75 in the second and 80 in the third?
Answer by JulietG(1812) About Me  (Show Source):
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No. The reason is that 46 words are crossed off the first list -- only 25 words are crossed off list two and 20 in list three, for a total of 45 crossed off words. Even if no words were in common for lists two and three, there would not be enough words to leave only 54 in list one.