IMPOSSIPUZZLES

1

“I just noticed your dad’s new phone number is four times ours,” said Stan. “And there’s something else funny about it – a real coincidence. If you switch the first two digits of his number, and also switch its other two digits, you get our number.”

He meant interchange, of course. What were the two numbers?

2

Walt watched as the three girls walked down the path. “Nice looking kids,” he said. “All more or less of an age.” “We’re proud of them,” Sam replied. “They’re evenly spaced, two years apart. Here’s something for you. Their ages total what my age is, and ten years ago they totalled only a third of that.” How old was Sam?

3

“What happened to all the zartyls?” asked Fred, looking around their pet shop. “The lizards from Mars?” Sally smiled. “You thought they’d never sell at nearly £2 each, but every kid who came in today wanted one.” “All the same price too,” her husband commented. “We should have charged more, anyway we did take £25.61 for the slimy things.” How many had he sold?

4

“So they gave you a three-figure number,” said George, looking at Alan’s new car. “How will you remember this one?” His friend chuckled. “It did take a bit of finding, but it’s really quite simple. The number is just twice the sum of the squares of its digits.” Simple for some! But what was the number?

5

“That’s interesting,” Ted exclaimed, putting down his pen. “I’m 20, you’re only a teenager, but do you know what a reciprocal is?” Bill nodded. “Of course I do. You write one over the number, like a third is the reciprocal of three.” “So listen to this,” Ted told him. “If you add the squares of the reciprocal of your age and mine, you get the square of the reciprocal of Ruth’s age.” What were the three ages?

6

“Fred’s new house?” Joe smiled. “It’s an easy number to remember.” “One of your gimmicks, I suppose,” Maud replied. “Well, let’s have it.” Joe nodded “All right. Five times the first figure, plus three times the last, gives one less than the product of its two digits.” So what was the number?