Every whole number from 1 to 50 belongs in the diagram. How many of the numbers belong outside all three circles?

Outside all three = odd numbers that are neither multiples of 7 nor perfect squares. There are 25 odd numbers; remove 7, 21, 35, 49 (odd multiples of 7) to get 21, then remove the odd squares 1, 9, 25 (49 is already gone) to get 18. 17 removes 49 twice, 21 forgets the squares, and 25 counts all the odd numbers.