A number is called square-free when no perfect square bigger than 1 divides it. How many of the numbers from 1 to 50 are square-free?

Only the squares 4, 9, 25 and 49 need checking: 16 and 36 are themselves multiples of 4, and every larger square is over 50. Multiples of 4 up to 50 number 12, of 9 number 5, of 25 number 2 and of 49 number 1. The single double count is 36, which is a multiple of both 4 and 9, so the spoiled numbers total 12 + 5 + 2 + 1 − 1 = 19 and the square-free ones number 50 − 19 = 31. The traps: 19 answers the opposite question; 32 forgets 49, the easiest square to overlook; and 30 counts 36 twice by skipping the subtraction.