Impossipuzzles

Test your problem-solving prowess and numerical know-how with these teasers. 1. Greg was checking the invoice. “You bought one hundred altogether, then,” he said. “A nice selection of the three qualities.” “That’s right, 79p, £1.25, and £1.97 each,” replied Mary. “It’s funny they came to exactly £100 for the lot.” How many at each price?

2. “Wow,” exclaimed Elsie when her husband came in. “New shoes, new tie, new shirt. I wonder what they cost.”

Mike grinned. “Only thirty pounds the lot,” he told her. “The shoes cost twice as much as the shirt and tie together, and the shirt just a third as much as the tie and shoes together.”

You work it out!

3. “Come on, Rory. Becky’s not a baby,” Ryan declared. “Three years ago she was as old as the years you’re older than her.”

Rory laughed. “I know, dad,” he replied. “But in three years she’ll be exactly two-thirds as old as I’ll be.” How old is Becky?

4. “Did you see that freight train this morning?” asked Isaac. “It was moving.”

“Sure, but it had three diesels,” Tom replied. “I figured it would pass completely through the Pallawa Tunnel in just two minutes doing 120 kilometres an hour.”

The boy nodded. “And the tunnel is exactly three kilometres long.”

How long was that train?

5. “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?