What 3 positive numbers give the same result when multiplied and added together?

A boy was carrying a basket of eggs. He fell down and all the eggs broke. When he went back home without any eggs his mother asked how many he had been carrying altogether in the basket. He was unable to remember.

But he was able to recall that when they were counted two at a time one was left, when counted three at a time one was left, when counted four at a time one was left, when counted five at a time none were left.

Can you tell how many eggs were broken?

There are 150 members in my club. We decided to have a ping pong tournament. All the members came forward to play in the game. Every time a member loses a game he is out of the tournament. There are no ties.

Can you tell how many games must be played in order to determine the champion?

A friend of mine emptied a box of matches on the table and divided them into three heaps, while we stood around him wondering what he was going to do next.

He looked up and said, “Well friends, we have here three uneven heaps. Of course you know that a match box contains altogether 48 matches. This I don’t have to tell you. And I am not going to tell you how many there are in each heap.”

“What do you want us to do?” one of the men shouted.

“Look well, and think. If I take off as many matches from the first heap as there are in the second and add them to the second, and then take as many from the second as there are in the third and add them to the third, and lastly if I take as many from the third as there are in the first and add them to the first—then the heaps will all have equal number of matches.”

As we all stood there puzzled he asked, “Can you tell me how many were there originally in each heap?” Can you?