Impossipuzzles

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

1. When Roy was half as old as Jane was when Roy was a third as old as Jane was when Roy was half as old as Jane is now, Jane was a third as old as Roy was when Jane was a year older than Roy is now. All ages referred to are or were whole numbers of years, so what are the ages of these two friends?

2. Walt watched as the three girls walked down the path. “Sweet looking kids,” he said. “All more or less of an age.” “We’re proud of them,” Sam replied. “They’re evenly spaced, two years apart. Here’s something for you. Their ages total what my age is, and ten years ago they totalled only a third of that.” How old was Sam?

3. The Professor slowed down as they entered Tulla Road. “What’s the number of their house?” he asked. “I think I told you.” Mary smiled. “Maybe it meant something to you, but not to me,” she replied. “You said it was twelve less than half its square.” That was enough, of course. What was the number?

4. “I just noticed your dad’s new phone number is four times ours,” said Stan. “And there’s something else funny about it - a real coincidence. If you switch the first two digits of his number, and also switch its other two digits, you get our number.” He meant interchange, of course. What were the two numbers?

5. “You can’t mistake the house,” said Andy. “We’ve got the only cedar tree on the street.” Les nodded. “That’s fine, but let’s have the number just to be sure.” “Okay.” Andy smiled. “If you add its two figures to it, you get its figures in reverse order.” What was it then?