In a game, the host chooses four distinct numbers and randomly orders them. A participant gets the prize if he or she can arrange the four numbers in the correct order. If each game participant gives a different order, what is the maximum number of players that can be present with no one winning the prize?

- 3
- 11
- 15
- 23
- 255

Answer is 23, but how to solve this.

You have 4 elements/numbers. The number of possible ways of arranging them is 4! (4 factorial) which is 24.

Now, only one of them is correct. So 23 of the arrangements are wrong. So if every person is choosing differently. Then you can have upto 23 people and everyone might still end up choosing one of the wrong answers. But if you have 24 people, and all of them choose differently, then one MUST have chosen the winning possibility since there are only 24 possible arrangements.