IMPOSSIPUZZLES

1

Jack was writing on a scrap of paper as he waited in the car. “See that number, Dad?” he said, pointing to the car ahead. “I got something on it.” “The four figures?” Harry shook his head. “That doesn’t look so very unusual to me.” The boy smiled. “It’s one less than six times the sum of the squares of its two halves.” What was it then?

2

“You’ve got more than me,” Jill told her brother. “Give me one of your toffees and then we’ll be even.” Jack shook his head. “Not on your life,” he replied. “But you give me one, and then I’ll have twice as many as you. That’s fair, as I’m nearly twice as old.” Hardly fair but how many did he have?

3

Ben studied the list. “There’s something wrong here,” he exclaimed. “We’ve not yet sold even 300 of those books in a month.” Fred checked. “You’re right,” he admitted. “I’ve got the figures down in reverse order, and that makes it about three times what it should be.” “Eleven less than three times, to be exact,” Ben told him. What was the correct number?

4

Sam seemed to be digging up his square tiled patio when I dropped in on him yesterday. “No, only making it smaller,” he told me. “I’m removing the outer tile all the way round. That’s taking away one tile less than the total that will remain.” The tiles were square and all the same size, so how many would he be removing?

5

“So you have a brother, eh?” said Harry. “That’s nice. How old is he?” “He’s only a baby,” Pam replied “If you multiply our ages you get three times what they add up to.” Hardly a straight answer, but how old was Pam?

6

Betty looked at the 20p pieces in her brother’s hand. “Is that all you’ve got?” she asked. “You had getting on for two pounds this morning.” “That’s right, and I’ve spent the rest,” Steve told her. “A quarter of what I spent is exactly a third of what I’ve got left.” How much had he spent?