A Modest Proposal

Okay, I’ll ask three questions, and if you miss one I get your house. Fair enough? Here we go:

A clock strikes six in 5 seconds. How long does it take to strike twelve?
A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?
A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?

Don’t be hasty — your house is on the line.

	Select Click for Answer
1. A clock strikes six in 5 seconds. How long does it take to strike twelve? Answer: Not 10 seconds, but 11 — one second per interval. 2. A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost? Answer: Not $1.00, but $1.05. 3. A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet? Answer: Neither — when they meet they’ll be equally distant from anywhere, n’est-ce pas? You’ll hear from my attorney.

October 4, 2007May 20, 2013 | Puzzles

“The Famous ‘Wheel Question'”

This question was proposed in the Scientific American, in 1868: ‘How many revolutions upon its own axis, will a wheel make in rolling once around a fixed wheel of the same size?’

The question brought to the editor of that paper many replies all claiming to have solved it. Yet the replies were about equally divided as to the number of revolutions, one part claiming one revolution and the other two revolutions. So much interest was manifested in it that Munn & Co. published The Wheel, June, 1868. It contains 72 pages, giving many of the solutions, illustrated by many diagrams.

— Miscellaneous Notes and Queries, August 1889

So who’s right?

	Select Click for Answer
The rolling wheel makes two revolutions. You can prove this to yourself using two coins with milled edges—hold one in place and roll the other around it.

October 2, 2007January 16, 2013 | Puzzles

A Physics Problem

You’re in a rowboat in a swimming pool, and you’re holding a cannonball. If you throw the ball into the pool, will the water level rise or fall?

	Select Click for Answer
It will fall. When the cannonball is in the boat, it displaces its weight in water. When it’s in the pool, it displaces only its volume.

September 12, 2007January 16, 2013 | Puzzles · Science & Math

Avoiding a Scandal

Three beautiful women and their jealous husbands want to cross a river, but the boat will hold only two people at a time. How can they arrange the crossing if no woman is to remain with a man unless her husband is present?

	Select Click for Answer
Mrs. A and Mrs. C cross Mrs. A returns Mrs. A and Mrs. B cross Mrs. B returns Mr. A and Mr. C cross Mr. A and Mrs. A return Mr. A and Mr. B cross Mrs. C returns Mrs. A and Mrs. B cross Mrs. A returns Mrs. A and Mrs. C cross Other solutions are possible, but all require at least 11 crossings. (The price of propriety!)

August 23, 2007January 16, 2013 | Puzzles

A Literary Knight’s Tour

The knight’s tour is a recreation familiar to chessplayers: Move a knight about an empty chessboard so as to visit each square exactly once.

On this board, each square contains a syllable. Collect them in the right order and you’ll compose a six-line quotation from Shakespeare. What is it?

(Hint: Start on e4, “to”.)

A Literary Knight's Tour

	Select Click for Answer
The quotation is from King John, Act IV, Scene II, lines 11-16: To gild refined gold, to paint the lily, To throw a perfume on the violet, To smooth the ice, or add another hue Unto the rainbow, or with taper-light To seek the beauteous eye of heaven to garnish, Is wasteful and ridiculous excess. The puzzle is taken from Miscellaneous Notes and Queries, January 1889.

August 21, 2007January 16, 2013 | Literature · Puzzles · Quotations

The Mutilated Chessboard

Take an ordinary chessboard and cut off two diagonally opposite corners. Now: Is it possible to tile the remaining 62 squares with 31 dominoes?

This calls for inspiration rather than trial and error. Most people see the solution immediately or not at all.

	Select Click for Answer
No, it can’t be done. Each domino covers two squares, a light one and a dark one. Therefore a board can be tiled perfectly only if it has an equal number of light and dark squares. The original board met this requirement, but we’ve removed two squares of the same color (diagonal corners). So the task is impossible.

July 17, 2007January 16, 2013 | Puzzles

“Ambiguous Lines”

First published in 1671, this anonymous verse came with a simple instruction that would render it into sense. Can you discover it?

I saw a peacock with a fiery tail
I saw a blazing comet drop down hail
I saw a cloud with ivy circled round
I saw a sturdy oak creep on the ground
I saw a pismire swallow up a whale
I saw a raging sea brim full of ale
I saw a venice glass sixteen foot deep
I saw a well full of men’s tears that weep
I saw their eyes all in a flame of fire
I saw a house as big as the moon and higher
I saw the sun even in the midst of night
I saw the man that saw this wondrous sight.
I saw a pack of cards gnawing a bone
I saw a dog seated on Britain’s throne
I saw King George shut up within a box
I saw an orange driving a fat ox
I saw a butcher not a twelvemonth old
I saw a great-coat all of solid gold
I saw two buttons telling of their dreams
I saw my friends who wished I’d quite these themes.

	Select Click for Answer
“Read with a comma after the first noun in each line”: I saw a peacock, with a fiery tail I saw a blazing comet, drop down hail I saw a cloud, with ivy circled round I saw a sturdy oak, creep on the ground I saw a pismire, swallow up a whale I saw a raging sea, brim full of ale I saw a venice glass, sixteen foot deep I saw a well, full of men’s tears that weep I saw their eyes, all in a flame of fire I saw a house, as big as the moon and higher I saw the sun, even in the midst of night I saw the man that saw this wondrous sight. I saw a pack of cards, gnawing a bone I saw a dog, seated on Britain’s throne I saw King George, shut up within a box I saw an orange, driving a fat ox I saw a butcher, not a twelvemonth old I saw a great-coat, all of solid gold I saw two buttons, telling of their dreams I saw my friends, who wished I’d quite these themes.

Click for Answer

July 11, 2007January 16, 2013 | Poems · Puzzles

A Self-Solving Chess Problem

self-solving chess problem

White to move. I won’t give the solution — try it out and you’ll see why.

(Composed by V. Röpke, Skakbladet, 1942.)

June 28, 2007November 10, 2017 | Puzzles

Kangaroo Words

Kangaroo words contain smaller versions of themselves. INDOLENT, for example, contains the letters I-D-L-E, in order. Can you find the hidden synonyms in each of these words?

ABIDE
ALLOCATE
ASSEVERATE
ASTOUND
CALUMNIES
CATACOMB
DEPOSITORY
DESTRUCTION
ENCOURAGE
HONORABLE
ILLUMINATED
INEFFECTIVE
REVOLUTION
SCOUNDREL
TRANSGRESSION
UMPTEENTH
UNSIGHTLY

	Select Click for Answer
ABIDE: BE ALLOCATE: ALLOT ASSEVERATE: AVER (also ASSERT) ASTOUND: STUN CALUMNIES: LIES CATACOMB: TOMB DEPOSITORY: DEPOT DESTRUCTION: RUIN ENCOURAGE: URGE HONORABLE: NOBLE ILLUMINATED: LIT INEFFECTIVE: EFFETE REVOLUTION: REVOLT SCOUNDREL: CUR TRANSGRESSION: SIN UMPTEENTH: NTH UNSIGHTLY: UGLY

June 26, 2007January 16, 2013 | Language · Puzzles

Regicide

A chess problem posed by Sam Loyd, published in Le Sphinx, 1866:

“Construct a game which ends with Black delivering discovered checkmate on move four.”

	Select Click for Answer
1.f3 e5 2.Kf2 h5 3.Kg3 h4+ 4.Kg4 d5#

June 6, 2007January 16, 2013 | Puzzles