Bertrand Meyer's technology+ blog

Alina was, as noted, on Pařížská (Paris avenue). Heeding the unknown voice, she started walking clockwise; she did not hesitate as to what this means since, conveniently, she was standing right next to a clock:

Luca was standing on the other side of the block. He too saw a clock:

Pařížská was built in the late nineteenth century, as Prague’s answer to the Paris Champs-Élysées; it cut through Josefov, the old Prague ghetto. Most of the old Josefov was destroyed at the time; among the buildings that survived were six synagogues, the famous cemetery, and the “Jewish Town Hall”. This last building had been reconstructed in the 18th century with a fancy clock using Hebrew letters and, as an homage to the right-to-left reading of Hebrew script, running in the opposite of the direction of ordinary clocks. The clock figures in Guillaume Apollinaire’s Alcools:

Tu ressembles au Lazare affolé par le jour
Les aiguilles de l’horloge du quartier juif vont à rebours
Et tu recules aussi dans ta vie lentement
En montant au Hradchin et le soir en écoutant
Dans les tavernes chanter des chansons tchèques

(You look like Lazarus scared by daylight
The hands of the Jewish quarter clock go backwards
And you too step back slowly through your life
As you walk up to the Hradčany and in the evening
Listen to Czech songs sung in taverns)

Luca started walking clockwise, according to the clock next to him; you know the rest.

Normal clocks all go the same way; the backwards clock is no more than a wink and a whim. Had Luca raised his eyes more:

he would have gone by one of the other, ordinary clocks, going in the same direction as Alina; and we would not have a story.

For the text of the puzzle see this earlier post.

Hints (by popular demand):

(1) Prague
(2) Guillaume Apollinaire

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.)