George Berkeley proposed that material things exist only because they are perceived to exist. In 1993, L.C. Rodó offered a suitably Berkeleyan puzzle in El Acertijo. Any piece, including a king, that is not regarded (attacked or guarded) by another piece disappears from the board. In the diagram above, every man is either attacked or guarded. But a single move (it may be by either White or Black) will set in motion a chain reaction in which all the pieces vanish from the board. What is the move?

From this position, how can White force Black to checkmate him in two moves?

Very little is known about Theophilus Thompson, a chess problemist who was born a slave in Maryland in 1855. That’s a pity, because his work is often beautiful. Here’s a sample:

White to mate in two.

Another retrograde chess puzzle by Raymond Smullyan. The pawn on g3 is of unknown color. During the game no piece has moved from a light square to a dark one or vice versa. Is the unknown pawn black or white?

A conundrum by John F. Collins, from the August 1968 issue of Word Ways:

Just then, someone came up from behind and put his hands over the Hatter’s eyes.

‘Guess who!’ said the newcomer in a thin, flat voice.

The Hatter froze for a moment and declared, rather coldly, ‘I have no use for practical jokers.’

‘Ha! Neither have I,’ retorted the stranger, still keeping his hands over the Hatter’s eyes.

At that, the Hatter seemed to accept the challenge of the game and started asking a series of questions in a manner that mingled hope with care.

Question: ‘Ahem. Would you, by chance, be in a black suit this evening?’

Answer: ‘I would, but not by chance, by design.’

Q. ‘I presume you’re a member of all the posh clubs?’

A. ‘Afraid not. Never even been invited.’

Q. ‘Surely you’re better than average?’

A. ‘Yes, indeed!’

Q. ‘Not spotted, I hope?’

A. ‘Knock wood.’

Q. ‘Married?’

A. ‘No, happy.’

Who is behind the Mad Hatter?

From a 19th-century British broadside:

Madam,

The love and tenderness I have hitherto expressed to
you is false, and I now feel that my indifference towards
you increases every day, and the more I see you the more
you appear ridiculous in my eyes, and contemptible–
I feel inclined and in every respect disposed and determined
to hate you. Believe me I never had any inclination
to offer you my hand. Our last conversation I assure you
left a tedious and wretched insipidity which has not
possessed me with an exalted opinion of your character,
your inconstant temper would make me miserable,
and if ever we are united, I shall experience nothing but
the hatred of my parents, added to everlasting dis-
pleasure in living with you. I have a true heart to bestow,
but however I do not wish you for a moment to think
it is in your service, as I could not give it to one more
inconstant and capricious than yourself, and one less
capable to do honour to my choice, and my family.
You, Madam, I beg and desire will be persuaded that I
think seriously, and you will do me a great favour to
avoid me. I shall excuse you taking the trouble to
give me an answer to this, as your letters are full of
nonsense and impertinence, and have not a shadow of
wit and good sense. Adieu, and believe me truly, I am
so averse to you, that it is impossible I should ever be,
Madam, your Affectionate Servant and Lover, R.G.

“By reading every other line of the above letter the true meaning will be found out.”

Raymond Smullyan devised this puzzle in 1957 while a student at the University of Chicago. The white king has just been knocked off the board during a legal game. Where was it standing?

From Henry Dudeney:

A banker in a country town was walking down the street when he saw a five-dollar bill on the curb. He picked it up, noted the number, and went to his home for luncheon. His wife said that the butcher had sent in his bill for five dollars, and, as the only money he had was the bill he had found, he gave it to her, and she paid the butcher. The butcher paid it to a farmer in buying a calf, the farmer paid it to a merchant who in turn paid it to a laundry woman, and she, remembering that she owed the bank five dollars, went there and paid the debt.

The banker recognized the bill as the one he had found, and by that time it had paid twenty-five dollars worth of debts. On careful examination he discovered that the bill was counterfeit. What was lost in the whole transaction, and by whom?

Suppose we fill Yankee Stadium with 50,000 people and ask them to spend the day shaking hands with one another.

Prove that, at the end of the day, at least two participants will have shaken hands with the same number of people.

By C.W. Wood. White to mate in two moves.