# The Bridges of Konigsberg

In old Konigsberg there were seven bridges:

Villagers used to wonder: Is it possible to leave your door, walk through the town, and return home having crossed each bridge exactly once?

Swiss mathematician Leonhard Euler had to invent graph theory to answer the question rigorously, but there’s a fairly intuitive informal proof. Can you find it?

# An International Riddle

The following riddles have the same answer. What is it?

• Scotland: “What is it that hangs high, and cries sore, has a head and no hair?”
• Wales: “I saw some object near to a town, in a very finely made palace between earth and heaven. It has a fine tail which almost reaches to the ground, and its tongue hangs in a very large skull. It spends most of its time in silence, but sometimes it calls its friends together.”
• France: “The more one pulls it, the more it cries out.”
• Lithuania: “A horse with a silver tail neighs on a high hill.”
• Serbia: “A dead mare doesn’t neigh, but when somebody pulls it by the tail, it neighs so that all men can hear it.”
• Newfoundland: “Round as a hoop, deep as a pail, never sings out till it’s caught by the tail.”
• Chile: “Señora Carolina likes to live in a high house, and if they pull her feet, she disturbs the inhabitants.”

# “The Dovetailed Block”

Another puzzle from Henry Ernest Dudeney:

“Here is a curious mechanical puzzle that was given to me some years ago, but I cannot say who first invented it. It consists of two solid blocks of wood securely dovetailed together. On the other two vertical sides that are not visible the appearance is precisely the same as on those shown. How were the pieces put together?”

# The Beale Ciphers

A secret hoard of \$20 million in gold and silver lies buried somewhere near Roanoke, Va. That’s according to a coded message left by adventurer Thomas Jefferson Beale in the 1820s:

I have deposited in the county of Bedford, about four miles from Buford’s, in an excavation or vault, six feet below the surface of the ground, the following articles, belonging jointly to the parties whose names are given in number “3,” herewith:

The first deposit consisted of one thousand and fourteen pounds of gold, and three thousand eight hundred and twelve pounds of silver, deposited November, 1819. The second was made December, 1821, and consisted of nineteen hundred and seven pounds of gold, and twelve hundred and eighty-eight pounds of silver; also jewels, obtained in St. Louis in exchange for silver to save transportation, and valued at US\$13,000.

The above is securely packed in iron pots, with iron covers. The vault is roughly lined with stone, and the vessels rest on solid stone, and are covered with others. Paper number “1” describes the exact locality of the vault, so that no difficulty will be had in finding it.

Unfortunately, no one has been able to decipher paper “1” or “3”, and a hundred years’ digging has turned up nothing. Is it a hoax? Who knows?

# A CIA Mystery

This is a little embarrassing — the CIA is having trouble decrypting a sculpture on its own grounds.

The piece, called Kryptos, was dedicated 15 years ago by American artist James Sanborn. It’s inscribed with four different messages, each encrypted with a different cipher. Sanborn would say only that the sculpture contains a riddle within a riddle, which will be solvable only after the four passages have been decrypted. He gave the complete solution to CIA director William H. Webster, who has passed it on to his successors.

The first three messages have been solved by CIA analysts, but the fourth — and the final riddle — remains open.

If you don’t want to work on this yourself, you can wait for Da Vinci Code author Dan Brown — reportedly it’s the subject of his next book.

# Alice’s Riddle

Everyone likes a good riddle. In Chapter 7 of Alice’s Adventures in Wonderland, the Mad Hatter poses a famous one: “Why is a raven like a writing desk?” Lewis Carroll intended that it should have no solution, but puzzle maven Sam Loyd offered these anyway:

• Because the notes for which they are noted are not noted for being musical notes.
• Poe wrote on both.
• Bills and tales are among their characteristics.
• Because they both stand on their legs, conceal their steels (steals), and ought to be made to shut up.

In 1896, Carroll proposed an answer himself: “Because it can produce a few notes, tho they are very flat; and it is nevar put with the wrong end in front!” (“Nevar” is “raven” spelled backward.)

# Three of a Perfect Pair

The Incompatible Food Triad is a culinary puzzle: Name three foods such that any two of them go together, but all three do not.

The puzzle originated with University of Pittsburgh philosopher Wilfrid Sellars, and some notable thinkers have taken a crack at it. Physicist Richard Feynman thought he’d stumbled onto a solution when he accidentally asked for milk and lemon in his tea (ick), but this doesn’t quite work, as one of the “good” pairs (milk and lemon) is bad.

Best attempts so far: salted cucumbers, sugar, yogurt; orange juice, gin, tonic. Honorable mention: “Get pregnant, and you can eat anything.”

# Stumper

Petals Around the Rose is a simple brain teaser with an impressive pedigree — here’s how Bill Gates responded to the puzzle when he first encountered it.

Newcomers are told that the name of the game is important. Someone rolls five dice and announces the “answer,” which is always zero or an even number.

That’s it. On each roll, the initiate has to give the correct answer before he’s told. When he can do this consistently, he becomes a Potentate of the Rose, pledged “to be a cruel and heartless wretch who will never divulge the secret of the game to anyone else.”

I’m told that the puzzle is a good index of intelligence — smart people take longer to figure it out.

# Theseus and the Minotaur

Theseus and the Minotaur is a series of Java-based puzzles in which you have to escape a maze without getting mashed by a computerized monster that moves predictably. There are 14 levels, and I can’t get past level 4.

The interesting thing is that the puzzles were designed by a computer, and they’re now being used in AI experiments at the National University of Ireland. So computers are now solving puzzles designed by other computers.

# Null and Loyd?

The stupendously brilliant Sam Loyd’s Cyclopedia of 5000 Puzzles, Tricks and Conundrums, with Answers, originally published in 1914, is now available online.

The riddles are pathetic (“What vine does beef grow on? The bo-vine”), but the rest is mostly terrific. One problem: Loyd withheld the solutions to some puzzles, offering a cash prize. He never followed up with the solutions, so they’ve become stumpers. Here’s one, called “The Trader’s Profit”:

A dealer sold a bicycle for \$50, and then bought it back for \$40, thereby clearly making \$10, as he had the same bicycle back and \$10 besides. Now having bought it for \$40, he resold it for \$45, and made \$5 more, or \$15 in all.

“But,” says a bookkeeper, “the man starts off with a wheel worth \$50, and at the end of the second sale has just \$55! How then could he make more than \$5? You see the selling of the wheel at \$50 is a mere exchange, which shows neither profit nor loss, but when he buys at \$50 and sells at \$45, he makes \$5, and that is all there is to it.”

“I claim,” says an accountant, “that when he sells at \$50 and buys back at \$40, he has clearly and positively made \$10, because he has the same wheel and \$10, but when he now sells at \$45 he makes that mere exchange referred to, which shows neither profit nor loss, and does not affect his first profit, and has made exactly \$10.”

“It is a simple transaction, which any scholar in the primary class should be able to figure out mentally, and yet we are confronted by three different answers,” Loyd says. “The first shows a profit of \$15, such as any bicycle dealer would; while the bookkeeper is clearly able to demonstrate that more than \$5 could not be made, and yet the President of the New York Stock Exchange was bold enough to maintain over his own signature that the correct profit should be \$10.”

I’m thinking the accountant’s right, but then I was a journalism major.