20 October 2009, 15:09

Yesterday’s New York Times carries an article by John Tierney about the 95th anniversary of the king of mathematical puzzles, Martin Gardner. The article is so well done that I will not even try a summary, referring you instead directly to it [1]. Just one detail worthy of note: when he undertook to write a monthly puzzle column for Scientific American at the age of 37, Gardner “had never taken a math course beyond high school. He had struggled with calculus and considered himself poor at solving basic mathematical puzzles, let alone creating them.”

Logical and mathematical puzzles are a great way to keep the mind alert; one of the attractions of going to meetings of IFIP Working Group 2.3 on Programming Methodology[2] is that members constantly tease each other with puzzles of diverse nature and difficulty; Rustan Leino, the group’s current secretary, keeps a fascinating collection on one of his Web pages [3].

It would be imprudent to promise anything like a “ monthly puzzle” here, but let me at least announce an “occasional series”, which is not too harsh a commitment, and propose the first installment today. This little teaser is definitely original: The Case of the Handsome Couple.

At a dinner, one couple stands out as particularly hansome; both the wife and the husband (Alina and Luca). Conversation turns to the inevitable question: “How did you two meet?”.

“ Interesting indeed”, says the wife. “It was love at first sight: I was walking and came face to face with Luca; on the spot, I knew he was the one.”

“Tell us more! Where and how?”

“It was in Prague. I was walking along the Pařížská avenue, this kind of Champs-Élysées of Prague, window-shopping at the luxury shops. Then my Blackberry rang; I picked it up. I heard an unknown voice, telling me to start walking clockwise around the block. For some reason I felt compelled to obey it; soon after I came face to face with him. You know the rest.”

The host turns to Luca: “How was it for you?”

“Will you believe me: exactly the same! I was actually, as we later reconstructed, on the other side of that same city block. Suddenly my iPhone rang and I heard that strange voice ordering me to keep walking clockwise around the block. And suddenly I find myself face to face with her! You see the result.”

It’s a normal city block, and they were both faithfully obeying the injunction to walk clockwise, yet met face to face. How was that possible?

References

[1] John Tierney: For Decades, Puzzling People With Mathematics, in New York Times, 19 October 2009, available here.

[2] IFIP WG 2.3, Programming Methodology: see the group’s Web page.

[3] Rustan Leino’s puzzle collection at research.microsoft.com/en-us/um/people/leino/puzzles.html. (Disclaimer: Rustan says he obtained two puzzles — originally from other sources —through me.)

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