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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He imagined connecting a heavy weight to a light one and dropping them together. Now Aristotle’s theory makes two contradictory predictions: The heavy weight should fall more slowly than normal, since the light weight now hinders it. The heavy weight should fall more quickly than normal, since the two connected weights now form one very heavy object. These can’t both be true, so Aristotle can’t be right. Instead the two weights must fall at the same rate. At the end of the final Apollo 15 moon walk, astronaut David Scott dropped a geologic hammer and a feather simultaneously, to test this idea without air resistance. Both hit the surface simultaneously. Mission controller Joe Allen wrote that this was “reassuring, considering both the number of viewers that witnessed the experiment and the fact that the homeward journey was based critically on the validity of the particular theory being tested.”

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September 24, 2013October 4, 2013 | Puzzles · Science & Math

Black and White

hoeg chess problem

By Niels Høeg. White to mate in two moves.

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1. Qd5! and the queen will mate. From Horsens Avis, Oct. 8, 1916.

September 20, 2013September 27, 2013 | Puzzles

Fish Story

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

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

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No heavy fish is unkind to children.

September 15, 2013September 20, 2013 | Puzzles

Black and White

ramsey chess problem

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

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1. Qf6! and Black can’t escape mate next move. From the Pittsburgh Gazette, 1903.

September 13, 2013September 20, 2013 | Puzzles

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?

September 6, 2013September 5, 2013 | Literature · Puzzles

Black and White

st. maurice chess problem

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

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White wins with the very quiet 1. Qg2! 1. … Kxf4 2. Bc7# 1. … Kf6 2. Bc3# 1. … Kd4 2. Qd5# 1. … Kd6 2. Qd5# From La Presse, 1896.

September 6, 2013September 13, 2013 | Puzzles

Black and White

havel chess problem

By Miroslav Havel. White to mate in two moves.

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White wins with the crazy-looking 1. Qc7! 1. … Kg6 2. Bd3# 1. … Kg8 2. Nf6# 1. … (N moves) 2. g8=Q# From Tidskrift för Schack, 1916.

August 30, 2013September 13, 2013 | Puzzles

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.

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Today.

August 29, 2013September 13, 2013 | Puzzles

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