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Puzzles

Ballot Measure

A Russian problem from the 1999 Mathematical Olympiad:

In an election, each voter writes the names of n candidates on his ballot. Each ballot is then placed into one of n+1 boxes. After the election, it’s noted that each box contains at least one ballot, and that if one ballot is drawn from each box, these n+1 ballots will always have a name in common. Show that for at least one box, there’s a name that appears on all of its ballots.

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Black and White

von holzhausen chess problem

By Walter Freiherr Von Holzhausen. White to mate in two moves.

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Black and White

dos santos chess problem

By Arthur Napoleão Dos Santos. White to mate in two moves.

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Edge Case

A circular table stands in a corner, touching both walls. A certain point on the table’s edge is 9 inches from one wall and 8 inches from the other. What’s the diameter of the table?

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Going Down

In antiquity Aristotle had taught that a heavy weight falls faster than a light one. In 1638, without any experimentation, Galileo saw that this could not be true. What had he realized?

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Black and White

hoeg chess problem

By Niels Høeg. White to mate in two moves.

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Fish Story

http://commons.wikimedia.org/wiki/File:Sharky.svg

A logic exercise by Lewis Carroll: What conclusion can be drawn from these premises?

  1. No shark ever doubts that it is well fitted out.
  2. A fish that cannot dance a minuet is contemptible.
  3. No fish is quite certain that it is well fitted out unless it has three rows of teeth.
  4. All fishes except sharks are kind to children.
  5. No heavy fish can dance a minuet.
  6. A fish with three rows of teeth is not to be despised.
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Black and White

ramsey chess problem

By Robert Henry Ramsey. White to mate in two moves.

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Two for One

Longfellow thought that Dante Gabriel Rossetti, the Victorian poet and painter, was two different people. On leaving Rossetti’s house he said, “I have been very glad to meet you, Mr. Rossetti, and should like to have met your brother also. Pray tell him how much I admire his beautiful poem, ‘The Blessed Damozel.’”

In Philosophical Troubles, Saul A. Kripke offers a related puzzle. Peter believes that politicians never have musical talent. He knows of Paderewski, the great pianist and composer, and he has heard of Paderewski the Polish statesman, but he does not know that they are the same person. Does Peter believe that Paderewski had musical talent?

Black and White

st. maurice chess problem

By Charles Ephrem St. Maurice. White to mate in two moves.

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Black and White

havel chess problem

By Miroslav Havel. White to mate in two moves.

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What Am I?

A riddle by Horatio Walpole:

Before my birth I had a name,
But soon as born I chang’d the same;
And when I’m laid within the tomb,
I shall my father’s name assume.
I change my name three days together
Yet live but one in any weather.

Dog Tired

Another puzzle by Boris Kordemsky: Jack London tells of racing from Skagway, Alaska, to a camp where a friend lay dying. London drove a sled pulled by five huskies, which pulled the sled at full speed for 24 hours. But then two dogs ran off with a pack of wolves. Left with three dogs and slowed down proportionally, London reached the camp 48 hours later than he had planned. If the two lost huskies had remained in harness for 50 more miles, he would have been only 24 hours late. How far is the camp from Skagway?

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Riddle

In the February 1926 issue of the National Puzzlers’ League publication Enigma, “Remardo” offered this mock-Latin verse:

Justa sibi dama ne
Luci dat eas qua re
Ibi dama id per se
Veret odo thesa me

What does it mean?

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Turn, Turn, Turn

A Russian problem from the 1999 Mathematical Olympiad:

Each cell in an 8×8 grid contains an arrow that points up, down, left, or right. There’s an exit at the top edge of the top right square. You begin in the bottom left square. On each turn, you move one square in the direction of the arrow, and then the square you have departed turns 90° clockwise. If you’re not able to move because the edge of the board blocks your path, then you remain on the square and it turns 90° clockwise. Prove that eventually you’ll leave the maze.

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Black and White

wiehe chess problem

By Christian Wiehe. White to mate in two moves.

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Black and White

adolphi chess problem

By Heinrich Leonhard Adolphi. White to mate in two moves.

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Black and White

nash chess problem

By Hugh H. Nash. White to mate in two moves.

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Mystery Guest

2013-08-07-mystery-guest

Who is this?

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Black and White

hermanson chess problem

By Halvar Hermanson. White to mate in two moves.

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Rock Music

From the 2001 Moscow Mathematical Olympiad:

Before you are three piles of stones. One contains 51 stones, one 49 stones, and one 5 stones. On each move you can either combine two piles into one or divide any pile with an even number of stones into two equal piles. Is it possible to end up with 105 piles, each containing a single stone?

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An Invitation

On Nov. 25, 1862, Abraham Lincoln sent this dispatch to Gen. Ambrose Burnside at Aquia Creek, Va.:

Can Inn Ale me withe 2 oar our Ann pas Ann me flesh ends NV Corn Inn out with U cud Inn heaven day nest Wed roe Moore Tom darkey hat Greek Why Hawk of abbott Inn B chewed I if.

What did it mean?

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Dictation

http://commons.wikimedia.org/wiki/File:Richard_Pigott_Vanity_Fair_9_March_1889.jpg

In 1887, Irish journalist Richard Pigott sold a series of letters to the Times of London. Purportedly written by Irish Parliamentary Party leader Charles Parnell, they seemed to show that Parnell had approved of a savage political assassination five years earlier. Parnell denounced the letters as a “villainous and bare-faced forgery.”

In the ensuing investigation, Parnell’s attorney asked Pigott to write a series of words and submit them to the court:

livelihood
likelihood
Richard Pigott
proselytism
Patrick Egan
P. Egan
hesitency

What was the point of this?

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Black and White

ognjanovic chess problem

By Zarko Ognjanovic, 1912. White to mate in two moves.

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