Among 100 students, 55 like cricket, 45 like hockey and 40 like tennis. 20 like both cricket and hockey, 15 like both hockey and tennis, 25 like both cricket and tennis, and 10 like all three games. How many of the 100 like none of the three?

Add the three single totals, take away the three pair totals, then put the triple total back once: 55 + 45 + 40 = 140, then 140 − (20 + 15 + 25) = 140 − 60 = 80, then 80 + 10 = 90 students like at least one game. So 100 − 90 = 10 like none. The traps: 20 leaves out the final step of adding the 10 back, and 30 subtracts the 10 instead of adding it — the students who like all three are removed three times by the pair totals, so exactly one copy has to be restored.