From Puzzles 101 by Nobuyuki Yoshighara. Don’t let the title mislead you – these puzzles are anything but beginner level!
“If you add up the nine numbers 1 – 9, you get 45. If you multiply the numbers 1-9, you get 362,880. Now suppose I have nine one-digit numbers. If I add all nine numbers and get 45, and if I multiply all nine numbers and get a product of 362,880, can I say that the numbers I have are 1,2,3,4,5,6,7,8, and 9?”