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?
25 eggs were broken.
There is only one way of finding a solution to this problem: Numbers which leave a remainder of 1, when divided by 2: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35
Numbers which leave a remainder of 1, when divided by 3: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Numbers which leave a remainder of 1, when divided by 4: 5, 9, 13, 17, 21, 25, 29, 33, 37
Numbers which leave no remainder when divided by 5: 5, 10, 15, 20, 25, 30, 35
The only number fulfilling the four conditions is 25.