IMPOSSI PUZZLES

1

“Well, if it isn’t Stan, of all people,” Doug exclaimed. “Fancy meeting here in the same hotel.” “Doug!” Stan cried. “It’s good to see you. What’s your room?” His friend gave the number. “No chance of a teaser on that.” “But there is,” Stan told him. “Both have three figures, but yours is the reverse of my number and my number is fivesixths of yours.” What was Doug’s number?

2

“Cheers!” said Andy, raising his glass. “Here’s to many more happy birthdays. I don’t mean to be rude, but how old are you?” The old lady smiled. “Ten years ago I was three times as old as I was when I was a quarter of what I hope to be ten years from now.” How old was she that day?

3

“Well, that’s the magic number,” Bob declared. “Now we only need some way to remember it.” Adam nodded. “I’ve got it,” he said. “It’s just one more than seventeen times the total of its digits.” Hardly an ideal solution to the problem! But what was the number?

4

Peter pointed to a printed notice on the fence as they passed a construction site. “That’s a funny number, Dad,” he said. “It’s the building permit.” “Funny?” Stan asked. “You mean because the first three figures are the same as the other three? “Partly, but that’s not all,” the boy replied. “It’s just seven times the square of each half.” What was the number?

5

John watched as the people came ashore. “Hi, Captain,” he said when Charlie appeared. “I reckon you had about a hundred passengers today.” “Not nearly that many.” The old man shook his head. “With twice as many adults, or three times as many kids, we would indeed have had exactly that number.” How many passengers had there been?

6

“They’re enormous,” said Ann, tipping out the grapefruit onto the table. “But is that all you got for £3?” Her husband smiled. “Cheap for that size, and they were priced singly. There were smaller ones at five pence each less, but they didn’t seem such good value.” “We could’ve got two more for the money,” Ann commented. “But you may be right.” How many had he bought?