Richard Howard Tom and Ray Magliozzi discuss cars, car repair and this week’s puzzler.
Tom and Ray Magliozzi, hosts of the wacky and ingenious NPR radio show Car Talk, discuss cars, car repair and logic “puzzlers.” The puzzlers are terrific — often classics at heart with a Car Talk twist. I thought it might be fun to try one on Numberplay.
Here’s the puzzler as it originally aired on Car Talk:
Cats, Dogs and Mice – Oh My!
RAY: I happened to find this puzzler the other day in my puzzler folder. It’s from Barry Lawber. And it’s from July ‘96. Here’s his puzzler:
You’re given $100 and told to spend it all purchasing exactly a hundred animals at the pet store. Dogs cost $15. Cats cost a buck, and mice are 25 cents each.
TOM: Let me get this straight. You have to spend exactly a hundred bucks and you end up with exactly a hundred animals?
RAY: Right. The other only other criterion is that you have to purchase at least one of each animal.
The question is, how many of each animal do you have to purchase to equal a hundred animals purchased at exactly a hundred dollars?
Solution
Update in next Monday’s Numberplay post.
Graphics related to reader comments
Tom and Ray used dogs at $15 and 4 mice for a dollar. Many other prices would have worked as well — over 1,000 combinations for dog prices from a $1 to $100 and mice from 1 to 100 for a dollar (cats remaining at $1). Leonard Kim figured this one out.
.Recap of the Circular Logic puzzle
Why are manhole covers round? We took a first crack at this question back on March 21 with our puzzle Why Are Manhole Covers Round? Among the many reasons: because manholes are round. (Sounds obvious. But it’s really not. Ravi explained.)
The discussion continued two weeks later with Circular Logic. Four questions.
Question 1. Why might round manhole covers be best in storms?
Answer: Storms create floods which pop manhole covers up out of their holes, according to Jason Chou from Mountain View Public Works. A round cover can most easily reseat itself. We were also surprised to learn that Mr. Chou’s crew would never roll a manhole cover, and that even a square manhole cover would never fall on someone working in the manhole.
Question 2. How many large hexagons can you make from material from four smaller hexagons? (The large fit just outside and the small just inside the same circle.)
Answer: Four small hexagons just inside a circle have the same area as three hexagons just outside a circle, as computed by Tom E and demonstrated graphically by Pummy Kalsi.
Question 3. How many circles would you need to melt and convert into same-diameter Reuleaux triangles in order to have enough material left over for one three-point hypocycloid?
Answer: The intended answer was two circles (computed by Pummy Kalsi) but Dr W found an error in the graphical hint: a three-point hypocycloid is formed by rolling a circle within another circle, and not by connecting three arcs.
Question 4. Consider the word “glow.” If you replace each letter with its counterpart in a mirror alphabet you will get the legitimate word “told.” What other words exhibit this same property?
Answer: Gary found 14 word pairs, including the palindrome girt/trig.
Notes
1. The puzzler Cats, Dogs and Mice – Oh My! aired on Car Talk’s Jan. 3, 2011 show. For more about Car Talk, visit www.cartalk.com.
2. Photo of Tom and Ray Magliozzi copyright © 2010 Dewey, Cheetham & Howe.
3. Thank you to Car Talk — and especially to Carly “High Voltage” Nix — for helping to make this puzzle happen.
4. Idea for a future puzzle? Please send to Numberplay@nytimes.com.
You can now download and print the popular variety puzzles from the Sunday magazine free online. Look below for links to this week’s puzzle as well as answers to last week’s.
Deb Amlen is a humorist and puzzle constructor whose work has appeared in The New York Times, The Washington Post, The Los Angeles Times, and other mainstream media. The puzzles she creates for The Onion and Bust Magazine, however, would never fly at The New York Times. Sorry, Mom.