In 1980 the Educational Testing Service offered this question on an aptitude test:
In pyramids ABCD and EFGHI shown above, all faces except base FGHI are equilateral triangles of equal size. If face ABC were placed on face EFG so that the vertices of the triangles coincide, how many exposed faces would the resulting solid have?
(A) Five (B) Six (C) Seven (D) Eight (E) Nine
Which is correct?
You’re standing with your friends Val and Colin when a stranger approaches and shows you 16 cards:
A♥ Q♥ 4♥
J♠ 8♠ 7♠ 4♠ 3♠ 2♠
K♣ Q♣ 6♣ 5♣ 4♣
A♦ 5♦
He shuffles the cards, selects one, and tells Val the card’s value and Colin the card’s color. Then he asks, “Do you know which card I have?”
Val says, “I don’t know what the card is.”
Colin says, “I knew that you didn’t know.”
Val says, “I know the card now.”
Colin says, “I know it too.”
What is the card?
White or Black to play and mate or self-mate in one move. That is, you must find a total of four moves from this position: a White move that mates Black instantly, a White move that forces Black to mate White instantly, and equivalent moves for Black.
“Memo: The above puzzle depends on a literal interpretation of the rule which provides that a Pawn on reaching the eighth square may become any piece irrespective of colour.”
WARNING: “This monstrosity is the production of an erratic solver who has been sorely tried, puzzled and perplexed all the year round by the many posers and problems which have appeared from time to time in the numerous Chess columns. His aesthetic patience, resignation, fortitude, culture and hope all at once breaking down, he set to work and with wrathful spirit, regardless of all problem construction, devised it more for the sake of retaliation and revenge than to give pleasure. To prove his spiteful character; when composing it, he was overheard repeating, ‘Since I cannot prove a lover to entertain these fair spoken days, I am determined to prove a villain.’ Consequently, gentle reader, we warn you not to attempt it, except indeed that you are the happy possessor of that knowledge wherein you are able to puzzle others. It may look beastly simple, but to any young solver who may be foolhardy enough to venture it we offer a few words of advice–carefully study the above memo and note that–but ‘hold enough,’ no more can we divulge, fearful of bringing the fiery wrath of the exasperated composer upon our devoted heads.”
This literary knight’s tour appeared originally in the Sussex Chess Magazine.
Start on d4, “Our”, and jump from square to square in the manner of a chess knight to assemble an eight-line verse. Like a chess knight’s tour, the correct solution visits every square on the board.
From Henry Dudeney:
Imagine a man going to the North Pole. The points of the compass are, as everyone knows:
He reaches the Pole and, having passed over it, must turn about to look North. East is now on his left-hand side, West on his right-hand side, and the points of the compass therefore
… which is absurd. What is the explanation?
We’ve seen chess problems in which White must mate in half a move and even in -1 moves.
In this one White must mate in 0 — he must deliver checkmate without touching any of his pieces:
How can he do this? Imagine that the position arose in an actual game.
The Earl of Yarborough offers you a wager. He’ll shuffle an ordinary deck and deal you 13 cards. If none of your cards ranks above 9, he’ll give you a thousand pounds. Otherwise you must give him one pound.
Should you accept?
A bit of conjuring adapted from Augustus de Morgan:
1. Think of a one-digit number and remember it. (Example: 4.)
2. Write down a number of any length. Jumble the figures into another number, and subtract one from the other:
3. Count the letters in your father’s first name, your state capital, and the name of your favorite Beatle, and add them together.
4. Multiply this number by 4 and its reverse by 5. Add these together, plus the number from step 1.
For example, suppose your father’s name is William, your state capital is Oklahoma City, and you choose Paul. That’s 23 letters in all, and 23 reversed is 32. (4 × 23) + (5 × 32) + 4 = 256.
5. Mix these figures (256) into the result from step 2 (4600708659), in any order, say 4560207086569.
Seeing nothing but this final list of figures, the conjurer names the one-digit number from step 1.
How does he do it?
From Henry Dudeney:
Here is a little military puzzle that may not give you a moment’s difficulty. It is such a simple question that a child can understand it and no knowledge of artillery is required. Yet some of my readers may find themselves perplexed for quite five minutes.
An inventor offered a new large gun to the committee appointed by our government for the consideration of such things. He declared that when once loaded it would fire 60 shots at the rate of a shot a minute. The War Office put it to the test and found that it fired 60 shots an hour, but declined it “as it did not fulfill the promised condition.”
“Absurd,” said the inventor, “for you have shown that it clearly does all that we undertook it should do.”
“Nothing of the sort,” said the experts. “It has failed.”
Can you explain this extraordinary mystery? Was the inventor, or were the experts, right?
