24 extremely intelligent people get invited to a really important party. Since it's really important after 9pm (the start time of the party) a guardian will guard the door to enter the party. All of the other 23 people arrive successfully at the party, but you get late and you encounter the guardian.
He says: "Imagine if I gave 23 hats of random colors to the 23 people in the party. I put them in a circle, so they can see the colors of the hats of all of the other people, but not the color of the hat they are wearing. They are not allowed to speak or communicate and they don't know how many hats of the same color exist, or how many different hat colors exist.
I told them that I gave the hats in a way where even by switching position in the circle randomly they still had a way to win.
Every 2 minutes a bell rings and who wants can come to me and tell me the color of their own hat. If 1 single person of the 23 people fail to tell their color they lose.
On the first bell ring 4 people come to me and guess the color correctly.
On the second bell 3 people come to me and all guess the color "red", which is correct.
On the third bell 0 people come to me.
On the fifth bell ring some people come to me and guess correctly their color.
On the sixth bell ring all of the remaining people come to me and manage to guess correctly.
If you can tell me how many people went out on the fourth bell ring I will let you in the party."