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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London would have reached the camp one day sooner if he’d covered 50 more miles at full speed. That means he’d have reached it two days sooner, and arrived on time, if he’d covered 100 miles at that speed. So at the end of the first day, 100 miles remained to reach the camp. He covered this in two days with three dogs, so with five dogs he would have covered 5/3(100) = 166 2/3 miles, going 66 2/3 miles beyond the camp in two days. That means a full team of five dogs covers 33 1/3 miles per day. London covered 33 1/3 miles on the first day and 100 miles after that, for a total of 133 1/3 miles. 08/30/2013 Wait, I screwed this up. It’s not correct to say that London covered 100 miles in two days with three dogs; I should have said instead that a full team would have covered 166 2/3 miles rather than 100, and that forgoing the extra 66 2/3 miles would have saved 48 hours, giving a full speed of 33 1/3 miles per day. So the answer was correct, but the solution was wrong. Sorry about that. (Thanks, Nick and Ben.)

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August 27, 2013September 13, 2013 | Puzzles

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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Just as I bid a man elucidate a square, I bid a maid persevere to do the same.

August 25, 2013August 30, 2013 | Puzzles

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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Suppose by way of contradiction that you’ll stay in the maze forever. Because the grid contains a finite number of squares, this means you’ll visit at least one square an infinite number of times. And because this square rotates after each visit, it follows that you’ll visit each of its adjacent squares an infinite number of times. By extension this means that you’ll visit every square on the board an infinite number of times. This includes the square in the upper right, which at some point will point out the exit. Hence it’s not possible to stay in the maze forever.

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August 24, 2013August 30, 2013 | Puzzles

Black and White

wiehe chess problem

By Christian Wiehe. White to mate in two moves.

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1. Qh1 and White will mate with 2. Qa1# or 2. Ng6#. From Nationaltidende, Jan. 27, 1884.

August 23, 2013August 30, 2013 | Puzzles

Black and White

adolphi chess problem

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

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1.Be1 Kb6 2.Rd6# From Der kleine Problemfreund, 1896.

August 16, 2013August 23, 2013 | Puzzles

Black and White

nash chess problem

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

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1.Qa2 Ke4 2.Qe6# From The Chess Amateur, 1910.

August 9, 2013August 16, 2013 | Puzzles

Mystery Guest

2013-08-07-mystery-guest

Who is this?

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Adolf Hitler. In 1945, before Hitler’s death was confirmed, the U.S. Secret Service posted these images throughout Germany to show how the dictator might disguise himself in order to escape capture.

August 7, 2013August 16, 2013 | History · Puzzles

Black and White

hermanson chess problem

By Halvar Hermanson. White to mate in two moves.

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1. Rb4! and the queen will mate. From Münchner Zeitung, 1912.

August 2, 2013August 9, 2013 | Puzzles

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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No. If at any point the number of stones in each pile is a multiple of the same odd number a, then this will remain true after any number of operations. On the first move we’re forced to create two piles of 100 and 5 stones (both divisible by 5), or 56 and 49 stones (both divisible by 7), or 51 and 54 stones (both divisible by 3). Whichever course we choose, all subsequent operations will produce piles divisible by that odd factor. This prevents us from producing piles of single stones.

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August 1, 2013August 9, 2013 | Puzzles

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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David Homer Bates, manager of the War Department Telegraph Office, explains: “By reading the above backward, observing the phonetics, and bearing in mind that flesh is the equivalent of meat, the real meaning is easily found”: If I should be in a boat off Aquia Creek at dark tomorrow (Wednesday) evening, could you without inconvenience meet me and pass an hour or two with me? — A. Lincoln “It cannot be said that this specimen exhibits specially clever work on the part of the War Department staff, nor is it likely that the Confederate operator, if he overheard its transmission, had much trouble in unraveling its meaning. As to this we can only conjecture.” Burnside understood it, and the two met. (David Homer Bates, “Lincoln in the Telegraph Office,” The Century Magazine, June 1907)

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July 28, 2013August 9, 2013 | Puzzles