Impossipuzzles

Test your problem-solving prowess and numerical know-how with these teasers.

1. Fred looked down over the boy’s shoulder. “That’s your Aunt Ada’s number,” he said. “What’s the idea?”

“I just figured out something on it,” Peter replied. “If you add its first digit to three times the square of the other two, you get just one less than her number.”

What was it?

2. Susan opened the box. “A frilly shirt and a fancy tie,” she exclaimed. “How much were they?”

“Not too much,” replied Bill. “But if you want, you can work out the prices yourself. If the shirt had cost £2.25 more it would have been two-thirds of the total cost, but if the tie had cost me £2.25 less it would have been just a quarter of the total.”

Well?

3. Bob pointed to an invoice on his desk. “Do you see anything funny about that five-figure serial number?” he asked.

“Let me try something,” replied Andy, scribbling on a scrap of paper. “Yes, it happens to be a perfect square.”

“That’s part of it,” Bob told him. “If you increase each digit by one, you get another perfect square.”

What was the serial number?

4. “Wow, all dolled up!” Mary exclaimed. “New coat, new trousers, new shoes. Did you win a lottery?”

“Come on, they weren’t so expensive,” Doug replied. “Only £102 the lot. The coat was just three times the shoes, and the trousers half as much as shoes and coat together.” What were the individual prices?