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Math & Logic · Ages 12–15

Riddle #157

In a class of 30 students, 18 play football and 15 play basketball. 5 students play neither sport. How many students play both?

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Answer: 8

30 − 5 = 25 students play at least one sport. 18 + 15 = 33 counts every both-player twice, so 33 − 25 = 8 play both.

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#158 Ten people meet at a party, and every person shakes hands with every other person exactly once. How many handshakes take place?
#145 Two trains start 300 miles apart and travel toward each other — one at 60 mph, the other at 40 mph. How long until they meet?
#146 The sum of three consecutive whole numbers is 72. What are the three numbers?

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