Tommy Smart was recently sent to a new school.  On the first day of his arrival the teacher asked him his age, and this was his curious reply:  “Well, you see, it is like this.  At the time I was born—­I forget the year—­my only sister, Ann, happened to be just one-quarter the age of mother, and she is now one-third the age of father.”  “That’s all very well,” said the teacher, “but what I want is not the age of your sister Ann, but your own age.”  “I was just coming to that,” Tommy answered; “I am just a quarter of mother’s present age, and in four years’ time I shall be a quarter the age of father.  Isn’t that funny?”

This was all the information that the teacher could get out of Tommy Smart.  Could you have told, from these facts, what was his precise age?  It is certainly a little puzzling.

49.—­Next-door neighbours.

There were two families living next door to one another at Tooting Bec—­the Jupps and the Simkins.  The united ages of the four Jupps amounted to one hundred years, and the united ages of the Simkins also amounted to the same.  It was found in the case of each family that the sum obtained by adding the squares of each of the children’s ages to the square of the mother’s age equalled the square of the father’s age.  In the case of the Jupps, however, Julia was one year older than her brother Joe, whereas Sophy Simkin was two years older than her brother Sammy.  What was the age of each of the eight individuals?

50.—­The bag of nuts.

Three boys were given a bag of nuts as a Christmas present, and it was agreed that they should be divided in proportion to their ages, which together amounted to 171/2 years.  Now the bag contained 770 nuts, and as often as Herbert took four Robert took three, and as often as Herbert took six Christopher took seven.  The puzzle is to find out how many nuts each had, and what were the boys’ respective ages.

51.—­How old was Mary?

Here is a funny little age problem, by the late Sam Loyd, which has been very popular in the United States.  Can you unravel the mystery?

The combined ages of Mary and Ann are forty-four years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann.  How old is Mary?  That is all, but can you work it out?  If not, ask your friends to help you, and watch the shadow of bewilderment creep over their faces as they attempt to grip the intricacies of the question.

52.—­Queer relationships.

“Speaking of relationships,” said the Parson at a certain dinner-party, “our legislators are getting the marriage law into a frightful tangle, Here, for example, is a puzzling case that has come under my notice.  Two brothers married two sisters.  One man died and the other man’s wife also died.  Then the survivors married.”