Impossipuzzles

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

1. “You bought two bits of land in Kalota?” Anne exclaimed. “But why triangles?”

Bert smiles. “I liked them, and they’re exactly similar in shape,” he replied. “All sides are perfect squares in kins. The longer side of the bigger one is 8 kins more than double its shortest side, and the short side of the smaller is 32 kins less than its middle side.” A strange investment, but what were the dimensions?

2. Ling On’s mother examined the boy’s purchase carefully. “Four chopsticks and a rice bowl,” she commented. “What did you pay?”

“One pound and forty pence altogether,” Ling On replied. “The chopsticks cost me just one pound more than the bowl.”

How much had the chopsticks cost him?

3. The three children had their marbles spread out on the floor when Jane looked in. “What a lot!” she exclaimed. “How many have you got there?” Betty smiled. “Gwen and I together have seventy-three,” she replied. “But Andy and Gwen have only sixty-two.” Andy looked up. “That’s right,” he said. “And Betty and I total sixty-five.”

How many did Andy have?

4. Bill noted the new number in his little book. “They’ve given you the same figures as my 4-digit number,” he said. “That’s funny.”

“So they have,” John agreed. “But our first and second digits are interchanged, and so are our third and fourth. As you say, the same four figures, but yours is four times my number.” What was Bill’s number?