In the game of Make 24 you start with 4 random numbers and try to find a way to make the number 24 by combining all four of the numbers in any order using any combination of addition, subtraction, multiplication, and division. The game is commonly played with a deck of cards using just the cards ace through 10, with ace counting as a 1.

Not all combinations of numbers can be successfully combined to make 24. Particularly those sets with pairs or triples of the same number may be "impossible" combinations. But if all four numbers are different, the odds are very good that a solution can be found. In fact, if you limit yourself to just the single digit numbers (1 through 9), then there are only two unique sets of four different numbers which cannot be combined to make 24. Can you find those two sets?