In a class of all boys, 18 boys like to play chess, 23 like to play soccer, 21 like biking and 17 like hiking. The number of those who like to play both chess and soccer is 9. We also know that 7 boys like chess and biking, 6 boys like chess and hiking, 12 like soccer and biking, 9 boys like soccer and hiking, and finally 12 boys like biking and hiking. There are 4 boys who like chess, soccer, and biking, 3 who like chess, soccer, and hiking, 5 who like chess, biking, and hiking, and 7 who like soccer, biking, and hiking. Finally there are 3 boys who like all four activities. In addition we know that everybody likes at least one of these activities. How many boys are there in the class?

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Asked Mar 4, 2020
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In a class of all boys, 18 boys like to play chess, 23 like to play soccer, 21 like biking and 17 like hiking. The number of those who like to play both chess and soccer is 9. We also know that 7 boys like chess and biking, 6 boys like chess and hiking, 12 like soccer and biking, 9 boys like soccer and hiking, and finally 12 boys like biking and hiking. There are 4 boys who like chess, soccer, and biking, 3 who like chess, soccer, and hiking, 5 who like chess, biking, and hiking, and 7 who like soccer, biking, and hiking. Finally there are 3 boys who like all four activities. In addition we know that everybody likes at least one of these activities. How many boys are there in the class?

 

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