Down, Over, Up

If you start at the North Pole and walk one mile south, one mile east, and one mile north, you’ll find yourself back at your starting point.

The North Pole is not the only point with this property on Earth’s surface. In fact, there are any number of such points. Where are they?

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“The Four Sevens”

Another puzzle from Henry Ernest Dudeney:

“In the illustration Professor Rackbrane is seen demonstrating one of the little posers with which he is accustomed to entertain his class. He believes that by taking his pupils off the beaten tracks he is the better able to secure their attention, and to induce original and ingenious methods of thought. He has, it will be seen, just shown how four 5’s may be written with simple arithmetical signs so as to represent 100. Every juvenile reader will see at a glance that his example is quite correct. Now, what he wants you to do is this: Arrange four 7’s (neither more nor less) with arithmetical signs so that they shall represent 100. If he had said we were to use four 9’s we might at once have written 99 9/9, but the four 7’s call for rather more ingenuity. Can you discover the little trick?”

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Source Forge

One of these Vermeers is a forgery. Which is it?

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The Bridges of Konigsberg

In old Konigsberg there were seven bridges:
Image: Wikimedia Commons

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?

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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.”
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“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?”

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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?