## 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.

## 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?

## 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?

## 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.

## 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?

## 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?

## 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?

## 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.

## 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?

## 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?

## Dictation

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?