IMPOSSIPUZZLES
1
“It’s funny about these two invoices,” said Charlie, pointing to them on his desk. “Each has a serial number that’s one more than eight times the square of its last two digits.” John looked. “6729? Is that just one more than eight times the square of 29?” “Sure,” Charlie replied. “And the other number works the same way.” What was the other?
2
“Was the bus crowded?” asked Sally. Jack smiled. “Not too bad, and there was only one stop on the way,” he replied. “It was funny about us passengers. We started with twice as many males as females. But at that stop seven men and one woman got off, and eleven women got on. Then we had twice as many females as males.” How many passengers was that?
3
Hetty paused in the gateway, gauging the distance to her quarry. “Just four leaps to reach him,” she thought. But Hector was alive to the danger. “I make seven bounds while she makes four leaps,” he told himself. “I’ve a good chance to make the old hole, although two of her leaps are as far as five of my bounds.” Then they both started! Poor Hector. The stupid hare had misjudged the distance to safety. Hetty only just caught him, but how many leaps did she have to make?
4
“Your cakes,” said Bert, tipping out the bag on the table. “They came to £1.80.” Jane looked. “They’re fine, and you did get more of the iced ones,” she commented. “What did you pay for those?” Her husband smiled. “As many pence each as the total number of cakes I bought,” he replied. “And I got as many of them as I paid in pence for each of the others.” How many of each sort?
5
“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?
6
Ling’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 replied. “The chopsticks cost me just one pound more than the bowl.” How much had the chopsticks cost?