IMPOSSIPUZZLES

1

“I got us a Kalotan rug,” Andy told his wife. “It took some finding as you wanted a true square.” Judy smiled. “What size is it?” “Well, I found three in one shop, different sizes, so I took the middle one,” Andy replied. “Mine was 720 square kils bigger than the smallest, but the same amount smaller than the largest, and the sides were all exact numbers of kils.” What were the respective dimensions?

2

“There’s a red scarf in the window,” said Jill. “I’d like two or three for presents, but do you have it in any other colour?” “Of course. Green and blue, but at different prices,” the girl replied. “A red and blue would be two pounds more than a green, a red and a green three pounds more than a blue, and a blue and a green four pounds more than a red.” What were the respective prices?

4

3

If my first were a 2, And my last were a 3, What I am would be 3 times The number I’d be. I’m only three digits, All odd, in a row. So what must I be? Don’t say you don’t know.

John picked up the girl’s sheet of paper. “That’s our new number, all four figures different,” he said. “What’s the idea?” “Something I figured out about it, Dad,” Maggie replied. “It’s just one less than twice the square of the difference between its two halves.” What is the new number?

5

Sarah picked up a pretty vase in the shop. “How many do you have like this?” she asked. The shopkeeper replied, “If we had half again as many as we’d have if we had half again as many as we have here, we’d have twice as many as we have and also half a vase.” How many vases did they have?

6

“Dad, I’ve thought of a very special 3-figure number,” said Terry. Tom smiled. “So that’s what you’ve been doing, when I thought you were on homework. Let’s have it, then.” “Okay.” The boy glanced at his working. “It’s exactly four times the sum of the squares of its digits.” What was the number?