Pythagorean Puzzle

pythagorean puzzleFrom here.


What If

What if Vallabhbhai Patel, not Nehru, had been India’s first Prime Minister?

Here is a cursory yet plausible answer from historian Ramachandra Guha:

“[T]he Congress would have become more right-wing (and pro-Hindu), with Nehru leaving to start an opposition party which, with his charisma (which far exceeded Patel’s), would have swept to power in the first general elections. So, I fear, this most remarkable and simultaneously most reviled of modern Indians would have become prime minister after all.”

nehru gandhi sardar

[Pic courtesy: Rediff]

Giant Jelly [Puzzle]

click to embiggen

[Source: DataGenetics, Pic Courtesy: CREATTICA]

Age of Dinosaurs

The first of the dinosaurs appeared around 231 million years ago, and they dominated earth for more than 135 million years. Homo Sapiens, on the other hand, evolved only around 200 thousand years ago. Here’s a chart to help put this into perspective (click to embiggen):


[Pic courtesy: Wikipedia]

Previous “Sense of Proportion” posts: IIIIIIIVVVI.

John & Julio

I found the following thought experiment stimulating:

Suppose two men, John and Julio, are heading to a job interview. Julio tells John: “I need this job more than you do. Please drop out of the race so I get it.” It’s perfectly reasonable for John to reply: “No. You’re a stranger and I don’t owe you anything.”

But suppose instead that John handcuffs Julio to a tree to prevent him from going to the interview. Julio says “Let me go. I deserve a shot at this job too.” At this point, it’s ludicrous for John to reply, “No. You’re a stranger and I don’t owe you anything.” Julio isn’t demanding help; he’s just demanding that John leave him alone.

And if John were to object, “You’re not leaving me alone. That job is MINE, and you’re trying to steal it from me!” we’d have to answer, “The job isn’t yours. It’s up to the owner of the business to decide who he wants to employ.”

All of this is obvious to any upright 10-year-old. You’re under no obligation to give your toys away to less fortunate kids, but you’re certainly not allowed to steal toys from less fortunate kids.

Unfortunately, if the victims happen to be born in another country, most adults don’t have the moral sense of a 10-year-old.

From here. Also read this article by Bryan Caplan, a fierce advocate of open borders, on the same topic: Why Should We Restrict Immigration? (pdf link)

The Outlawed Letters

k atatürk

“There is a story about Mustafa Kemal Atatürk practising his signature in the Latin alphabet. The image is incongruous: the most powerful man in Turkey sits frowning over his own name, breaking in the unfamiliar strokes like a schoolboy. He had decreed in 1928 that Turkish would now be written in Latin rather than Arabic script – severing ties with the Ottoman past and making a generation of readers illiterate. In 1934 he passed a law requiring everyone to adopt a surname: Turks at the time tended to go by titles, patronymics or the name of their profession. It’s unclear how Kemal came by his name (he tacked on ‘Father of the Turks’ after 1934; it’s still illegal for anyone else to use it), but as for romanising his initials, the story goes that he tried spelling it first with a Q, then with a K – and deciding that he preferred the latter, banned the letter Q from the alphabet. The story is apocryphal; Kemal’s signature (now one of the most popular tattoos in Turkey) was designed by Hagop Çerçiyan, an Armenian calligrapher. And while it’s true that the letter Q was outlawed for 85 years, from 1928 until last month, the reason for the ban had little to do with aesthetic bias or onomastic whim.” [More here]

Apparently, the 85 year-old ban on W, Q, and X may end soon. Also read my old post on linguistic nationalism.

The Defective Doyle [Puzzle]

Shurl and Watts, at a base on Pluto, are in charge of distributing doyles to more distance outposts. Doyels are the size of peas, all identical, each weighing precisely 1 gram. They are indispensable in hyperspace propulsion systems.

Doyles come in cans of 100 doyles each, and shipments are made up of six cans at a time. The Pluto base has a sensitive spring scale capable of registering fractions of milligrams.

One day, a week after a shipment of doyles, a radio message came from the manufacturing company in Hong Kong, “Urgent. One can is filled with defective doyles, each with an excess weight of 1 milligram. Identify the can and destroy its doyles at once.”

“I suppose,” said Watts, “we’ll have to make six weighings, one doyle from each can.”

“Not so, my dear Watts,” said Shurl. “we can identify the can of defectives with just one weighing.” [And then he goes on to explain how this can be achieved using a single weighing.]

“How absurdly simple!” exclaimed Watts, while Shurl shrugged.

A month later, after the next shipment, another message arrived: “Any of the six cans, perhaps all of them, may be full of defective doyles, each 1 milligram overweight. Identify and destroy all defective doyles.”

“This time,” said Watts, “I suppose we’ll have to weight separately a doyle from each can.”

Shurl put his fingertips together and gazed at a picture of Isaac Asimov on the wall. “A capital problem, Watts. No, I think we can still do it in just one weighing.”

What algorithm does Shurl have in mind?

[From Mathematical Puzzle Tales by Martin Gardner]

PS: The solution of the first weighing problem (one defective can) is actually provided in the original text of this puzzle. I’ve removed it for those who are not familiar with the solution and want to give it a shot.

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