# Heart and Head

Just offering this as a curiosity:

It was devised by the late Japanese cryptogramist Kyoko Ohnishi, and praised by puzzle maven Nob Yoshigahara. If each letter stands for a unique digit, what product is encoded here?

When this appeared in MIT Technology Review in November 2012, it attracted 20 responses, but it appears that all of them used computers to find the solution. If there’s a way to reason it out, I don’t think anyone has found it yet.

If we assume that neither of the factors has a leading zero, and that the partial products have five and four digits, as shown, then the solution is unique. I’ll put it in the spoiler box below, in case you want to work on it yourself.

# Podcast Episode 73: The Tichborne Claimant

In 1854, English aristocrat Roger Tichborne disappeared at sea. Twelve years later, a butcher from Wagga Wagga, Australia, claimed he was the long-lost heir. In this week’s episode of the Futility Closet podcast, we’ll tell the sensational story of the Tichborne claimant, which Mark Twain called “the most intricate and fascinating and marvelous real-life romance that has ever been played upon the world’s stage.”

We’ll also puzzle over why family businesses are often more successful in Japan than in other countries.

Sources for our feature on the Tichborne claimant:

Rohan McWilliam, The Tichborne Claimant: A Victorian Sensation, 2007.

Robyn Annear, The Man Who Lost Himself: The Unbelievable Story of the Tichborne Claimant, 2011.

This week’s lateral thinking puzzle is from Paul Sloane and Des MacHale’s 2014 book Remarkable Lateral Thinking Puzzles. There’s a fuller explanation (with spoilers!) in Dan Lewis’ Now I Know newsletter.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

# Comparative Zoology

In 1866, writing in the Virginia City Territorial Enterprise, Mark Twain accused San Francisco police chief Martin Burke of corruption, and “some leather-head” misinterpreted the column to suggest that Burke kept a mistress. Twain wrote to the San Francisco Examiner with a clarification:

EDITOR EXAMINER:–You published the following paragraph the other day and stated that it was an ‘extract from a letter to the Virginia Enterprise, from the San Francisco correspondent of that paper.’ Please publish it again, and put it in the parentheses where I have marked them, so that people who read with wretched carelessness may know to a dead moral certainty when I am referring to Chief Burke, and also know to an equally dead moral certainty when I am referring to the dog:

‘I want to compliment Chief Burke — I do honestly. But I can’t find anything to compliment him about. He is always rushing furiously around, like a dog after his own tail — and with the same general result, it seems to me; if he (the dog, not the Chief,) catches it, it don’t amount to anything, after all the fuss; and if he (the dog, not the Chief,) don’t catch it it don’t make any difference, because he (the dog, not the Chief,) didn’t want it anyhow; he (the dog, not the Chief,) only wanted the exercise, and the happiness of “showing off” before his (the dog’s, not the Chief’s,) mistress and the other young ladies. But if the Chief (not the dog,) would only do something praiseworthy, I would be the first and the most earnest and cordial to give him (the Chief, not the dog,) the credit due. I would sling him (the Chief, not the dog,) a compliment that would knock him down. I mean that it would be such a first-class compliment that it might surprise him (the Chief, not the dog,) to that extent as coming from me.’

He added: “I think that even the pupils of the Asylum at Stockton can understand that paragraph now.”

# “Inventory”

Four be the things I’d been better without:
Love, curiosity, freckles, and doubt.

— Dorothy Parker

# Black and White

By M. Techritz. Place the black and white kings on the board so that White can mate in one move.

# Child of Fortune

You exist because of a fragile string of circumstances: Your parents had to meet and procreate at a particular time, and so did their parents, and so on. If any of these things had not happened, you would not be here.

But the past that produced you also produced a whole series of historical and natural calamities — the Holocaust, World War I, and slavery, for example. Very likely those calamities influenced the delicate causal chain that leads to your existence. Without them, your ancestors would not have met and had children when they did. Properly speaking, then, shouldn’t you regret your own existence, since it required these tragedies to bring it about?

University of Haifa philosopher Saul Smilansky writes: “A ‘package deal’ is involved here: those events, together with oneself; or, the absence of the historical calamity, and the absence of oneself. So, all considered, ought one to prefer never to have existed, and to regret that one exists?”

(Saul Smilansky, “Morally, Should We Prefer Never to Have Existed?”, Australasian Journal of Philosophy 91:4, 655-666.)

# Reminder

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# Half of Everything

If two people want to split up amicably, the easiest solution is to divide their assets equally, with each partner getting 0.5. But suppose that one partner goes to a lawyer who charges a fee f but promises to get more, by an amount m + f, leaving his client better off by the amount m. If this happens, then the second partner will get only 0.5 – mf. If the second partner engages their own lawyer then the split is equal again, except that now the lawyers’ fees must be paid:

This is an example of the so-called prisoner’s dilemma: Both sides would be better off if they left the lawyers out of it, but if one engages a lawyer than the other had better do so as well.

Now suppose that each partner can choose the amount of lawyer time to buy, and that they get a payoff that’s proportional to the amount they spend. If one spends x on lawyers and the other spends y, each measured as a fraction of the total assets, then the first partner should receive an amount given by:

$\frac{x(1-x-y)}{x+y}$

An industrious divorcee can now use calculus to maximize this expression, varying x and keeping y constant. The optimum value of x turns out to be $\sqrt{y}-y$. If my partner spends 9%, or 0.09, of our assets on lawyers, then I should spend $\sqrt{0.09}-0.09=0.21$. Then my partner will get 0.21 of the assets, and I’ll get 0.49, and the lawyers get the rest.

Well, now what? Knowing all this, what’s our best course? If we could trust each other then we’d each pay a pittance on lawyers and get nearly 0.5 each. But I’m aware that if you pay a millionth and I pay a thousandth (still nearly a pittance), I’ll get nearly 99.9% of our assets. And simply resolving to outspend you won’t work: If you spend 0.36 then I should spend 0.24; I’ll come away with less than you, but this is the best I can do.

“Looking at the graph of $x=\sqrt{y}-y$, above, we (the author and reader) see that y = 0.25 gives us x = 0.25, and this gives us a sort of stability,” writes Anthony C. Robin in the Mathematical Gazette. “Neither partner can pull a fast one over the other, and it results in the assets being equally shared between us, them, and the lawyers. No doubt this is the reason why lawyers are so rich in our society!”

(Anthony C. Robin, “How Lawyers Make a Living,” Mathematical Gazette 88:512 [July 2004], 313-315.)

# A Grave Irony

“I have seen a thousand graves opened, and always perceived that whatever was gone, the teeth and the hair remained of those who had died with them. Is this not odd? They go the very first things in youth and yet last the longest in the dust.” — Lord Byron, letter to John Murray, Nov. 18, 1820

ditation
n. enrichment

improficuous