IMPOSSIPUZZLES

1

Harry looked at the scrap of paper in the boy’s hand. “That 5-figure number?” he asked. “It doesn’t mean a thing to me. Should it?” “I suppose not, Dad, but it is rather special,” Ted replied. “Half of it is one less than the square of our house number, and a third of it is one less than the square of Aunt Betty’s number.” What was Betty’s house number?

2

“You and Janice have birthdays in May,” said Steve. “What dates?” John smiled. “Well, I’m a day older than Janice, so work it out yourself,” he replied. “In a leap year, the square of the number of days after my birthday is exactly four times the square of the number of days prior to her birthday.” What were their birthdays?

3

“You’ve got a lot of marbles,” said Sam. “But only reds, greens and blues. How many in all?” Alan smiled. “You can work it out, Dad,” he replied. “The blues are nine more than a third of the reds, the reds are a third of the total, and I’ve got twice as many blues as greens.” Well?

6 4

They’ve just found a man in Baku Whose age is his wife’s age plus two. The sum of their squares, So the paper declares, Is 5 times a square – and it’s true. What are the ages of this husband and wife?

5

“What’s the price of this?” Tom asked. “I left my glasses at home.” Bill looked, and thought a moment. “The pennies are two thirds of the pounds, Dad,” he replied. “If the pounds were pennies and the pennies pounds it would be about three pounds less.” What was the price?

The boy undid the wrapping on the present. “A goldfish, Dad,” he exclaimed. “It must have cost a lot.”

Dad smiled. “Not too much. If the fish had been a pound more it would have cost three times as much as the bowl. If the bowl had been fifty pennies less it would have been a quarter the price of the goldfish.” What had been the total cost?