Suppose I show you two old coins. One is dated 51 B.C., and the other is marked George I. Which is authentic?
If you were a British soldier in Malta in the 19th century, you might receive this card from a local dram-shop:
What does it mean?
From Amusements in Mathematics by Henry Ernest Dudeney (1917):
The men in the illustration are disputing over the liquid contents of a barrel. What the particular liquid is it is impossible to say, for we are unable to look into the barrel; so we will call it water. One man says that the barrel is more than half full, while the other insists that it is not half full. What is their easiest way of settling the point? It is not necessary to use stick, string, or implement of any kind for measuring. I give this merely as one of the simplest possible examples of the value of ordinary sagacity in the solving of puzzles. What are apparently very difficult problems may frequently be solved in a similarly easy manner if we only use a little common sense.
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.
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?
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?
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?
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”.)
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.
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.
White to move. I won’t give the solution — try it out and you’ll see why.
(Composed by V. Ropke, Skakbladet, 1942.)
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?
A chess puzzle set on a Mobius strip, via Lawrence Kesteloot’s puzzles page.
There are no pieces on the hidden sides, and don’t worry about the direction of the black pawn. White to move and mate in two.
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.”
“Christopher Columbus’s Egg Puzzle,” as it appeared in Sam Loyd’s Cyclopedia of Puzzles (1914):
The famous trick-chicken, Americus Vespucius, after whom our great country was named, showed a clever puzzle wherein you are asked to lay nine eggs so as to form the greatest possible number of rows of three-in-line. King Puzzlepate has only succeeded in getting eight rows, as shown in the picture, but Tommy says a smart chicken can do better than that!
On a train, Smith, Robinson, and Jones are the fireman, the brakeman, and the engineer (not necessarily respectively). Also aboard the train are three passengers with the same names, Mr. Smith, Mr. Robinson, and Mr. Jones.
(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.
Who is the engineer?
Nothing is better than eternal happiness.
Eating a hamburger is better than nothing.
Therefore, eating a hamburger is better than eternal happiness.
“In an old church in Westchester county, N.Y., the following consonants are written beside the altar, under the Ten Commandments. What vowel is to be placed between them, to make sense and rhyme of the couplet?”
– Charles Bombaugh, Facts and Fancies for the Curious From the Harvest-Fields of Literature, 1860
Another puzzle from Henry Ernest Dudeney, The Canterbury Puzzles, 1908:
“Inside a rectangular room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as at A, and a fly is on the opposite wall, 1 foot from the floor in the centre, as shown at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course the spider never drops or uses its web, but crawls fairly.”
Can you make three cuts in a square of cloth and rearrange the pieces to form an equilateral triangle?
The “Death’s-head Dungeon,” from Henry Dudeney’s Canterbury Puzzles (1908), in which a youth rescues a noble demoiselle from a dungeon belong to his father’s greatest enemy:
“… Sir Hugh then produced a plan of the thirty-five cells in the dungeon and asked his companions to discover the particular cell that the demoiselle occupied. He said that if you started at one of the outside cells and passed through every doorway once, and once only, you were bound to end at the cell that was sought. Can you find the cell? Unless you start at the correct outside cell it is impossible to pass through all the doorways once, and once only.”
Retrograde analysis involves looking into a chess game’s past, rather than its future. Here’s an example from Henry Ernest Dudeney (1917):
“Strolling into one of the rooms of a London club, I noticed a position left by two players who had gone. This position is shown in the diagram. It is evident that White has checkmated Black. But how did he do it? That is the puzzle.”
The solution is unique. Can you find it?
Here’s a valentine written by Edgar Allan Poe in 1846. His sweetheart’s name is hidden in it — can you find it?
For her these lines are penned, whose luminous eyes,
Brightly expressive as the starts of Leda,
Shall find her own sweet name that, nestling, lies
Upon the page, enwrapped from every reader.
Search narrowly these words, which hold a treasure
Divine — a talisman, an amulet
That must be worn at heart. Search well the measure –
The words — the letters themselves. Do not forget
The smallest point, or you may lose your labor.
And yet there is in this no gordian knot
Which one might not undo without a sabre
If one could merely comprehend the plot.
Upon the open page on which are peering
Such sweet eyes now, there lies, I say, perdus,
A musical name oft uttered in the hearing
Of poets, by poets — for the name is a poet’s too.
In common sequence set, the letters lying,
Compose a sound delighting all to hear –
Ah, this you’d have no trouble in descrying
Were you not something, of a dunce, my dear –
And now I leave these riddles to their Seer.