Futility Closet

Solution to The Locked Gift, from Monday:

I put the necklace in a box, add a padlock, and send it to my wife.

She adds a second padlock and mails it back.

I remove my padlock and send her the box, and she opens it.

Dartmouth mathematician Peter Winkler writes, "This solution is not just play; the idea is fundamental in Diffie-Hellman key exchange, a historic breakthrough in cryptography."

When, at the General Peace of 1814, Prussia absorbed a portion of Saxony, the king issued a new coinage of rix dollars, with their German name, EIN REICHSTAHLER, impressed on them. The Saxons, by dividing the word, EIN REICH STAHL ER, made a sentence of which the meaning is, 'He stole a kingdom!'

– William T. Dobson, Poetical Ingenuities and Eccentricities, 1882

I want to mail a necklace to my wife, but anything sent through the mail will be stolen unless it's sent in a padlocked box. A box can bear any number of padlocks, but neither of us has the key to a lock owned by the other. How can I mail the necklace safely to my wife?

I'll give the answer tomorrow.

zenzizenzizenzic
n. a number raised to the eighth power

A medal struck of the 17th-century Swedish king Gustavus Adolphus included this motto:

ChrIstVs DuX ergo trIVMphVs

Rearrange the capital letters and you get MDCXVVVII, or 1627, the year in which the medal was stamped.

That's a chronogram, and a pretty tame one, as these things go. In 1634 the Society of Jesuits at Brussels composed a remarkable congratulation to Ferdinand on his arrival in the Netherlands as governor; it contains 100 hexameters, every one of which is a chronogram adding to 1634:

AngeLe CoeLIVagI MIChaeL, LVX VnICa CaetVs.
Pro nVtV sVCCInCta tVo CVI CVnCta MInIstrant.
SIDera qVIqVe poLo gaVDentIa sIDera VoLVVnt. …

"Genius," wrote Thomas Carlyle, "is an infinite capacity for taking pains."

Take two pieces of string or tape, and round the wrists of two persons tie the string, as shown in Fig. 19. It adds to the amusement of the puzzle if one of the persons is a lady and the other a gentleman. The puzzle is for them to liberate themselves, or for any one else to release them without untying the string. To do this, B makes a loop of his string pass under either of A's manacles, slips it over A's hands, and both will be free. Reverse the proceeding, and the manacles are again as before.

– Cassell's Complete Book of Sports and Pastimes, 1896

This pouch contains two counters. Each is either black or white. Without opening the pouch, prove that one is black and one white.

The probability that the pouch contains two black counters is 1/4; a black and white counter 1/2; and two white counters 1/4.

The chance of drawing one black counter in each case is 1, 1/2, or 0.

So if we combine these values we'll get the probability of drawing one black counter from the pouch:

(1/4 × 1) + (1/2 × 1/2) + (1/4 × 0) = 1/2

And if the probability of drawing a black counter is 1/2, then the pouch must contain one black and one white counter. Q.E.D.

(J.A.H. Hunter, after Lewis Carroll)

A queer dream or illusion had haunted Lincoln at times through the winter [of 1860]. On the evening of his election he had thrown himself on one of the haircloth sofas at home, just after the first telegrams of November 6 had told him he was elected President, and looking into a bureau mirror across the room he saw himself full length, but with two faces. … A few days later he tried it once more and the illusion of the two faces again registered to his eyes. But that was the last; the ghost since then wouldn't come back, he told his wife, who said it was a sign he would be elected to a second term, and the death pallor of one face meant he wouldn't live through his second term.

– Carl Sandburg, Abraham Lincoln: The Prairie Years, 1926

Where can you draw potable seawater even when no land is in sight?

Offshore of the mouth of the Amazon, which supplies 20 percent of the fresh water entering the world's oceans.

Solution to Monkey and Pulley, from Thursday:

We find the age of the monkey works out at 1.5 years, and the age of the mother 2.5 years, and the monkey therefore weighing 2.5 lbs., and the weight the same. Then we soon discover that the rope weighed 1.25 lbs., or 20 oz.; and, as a foot weighed 4 oz., the length of the rope was 5 feet.

(From Henry Dudeney.)