Wei-Hwa Huang offered this brilliant crossword in the May 2008 issue of Word Ways:
Across
1 Sticks
6 Farm animals
7 Ogles
8 Leisure
9 Ride
Down
1 Soothe
2 Peaceful
3 Reserved
4 Untroubled
5 Pacify
Puzzles
The Clockwise Ant
A problem by Argentinian puzzlist Jaime Poniachik, from the February 1992 issue of Games magazine:
An ant crawls onto a clock face at the 6 mark just as the minute hand is passing 12. She begins crawling counterclockwise around the face’s circumference at a uniform speed. When the minute hand passes her, she reverses course and crawls clockwise without changing her speed. Forty-five minutes after her first encounter with the minute hand, it passes her a second time and she departs. How much time did she spend on the clock face?
Desperate Measures
A joke chess problem by Bohuslav Sivák, from the Bratislavan newspaper Pravda, Dec. 29, 1972. White can mate in two moves by resorting to a drastic stratagem. What is it?
Square Diamonds
A puzzle by Henry Dudeney, from 1931:
“Here you have the two to the ten of Diamonds, inclusive. Can you re-arrange them, still retaining the shape of the figure, so that the ‘pips’ total eighteen, across and down, in each line, and also diagonally from the corners?”
Fanciful Creatures
In What Is the Name of This Book? (1986), Raymond Smullyan describes two curious denizens of the Forest of Forgetfulness. The Lion lies on Mondays, Tuesdays, and Wednesdays, and the Unicorn lies on Thursdays, Fridays, and Saturdays. Each tells the truth on the days it doesn’t lie.
One day Alice encounters the two of them resting under a tree. They tell her:
Lion: Yesterday was one of my lying days.
Unicorn: Yesterday was one of my lying days too.
“From these two statements, Alice (who was a very bright girl) was able to deduce the day of the week. What day was it?”
The Number Checks Puzzle
From Henry Dudeney’s Amusements in Mathematics, 1917. Without removing these checks from their ring, divide them into three groups so that the first group multiplied by the second makes the third. For example, one valid try might be 28, 907, 15463, except that 28 × 907 doesn’t equal 15463.
“Of course, you may have as many of the checks as you like in any group. The puzzle calls for some ingenuity, unless you have the luck to hit on the answer by chance.”
Charlie’s Birthday
A puzzle by National Security Agency mathematician Stephen C., from the agency’s July 2015 Puzzle Periodical:
Charlie presents a list of 14 possible dates for his birthday to Albert, Bernard, and Cheryl.
- Apr 14, 1999
- Feb 19, 2000
- Mar 14, 2000
- Mar 15, 2000
- Apr 16, 2000
- Apr 15, 2000
- Feb 15, 2001
- Mar 15, 2001
- Apr 14, 2001
- Apr 16, 2001
- May 14, 2001
- May 16, 2001
- May 17, 2001
- Feb 17, 2002
He then announces that he is going to tell Albert the month, Bernard the day, and Cheryl the year.
After he tells them, Albert says, “I don’t know Charlie’s birthday, but neither does Bernard.”
Bernard then says, “That is true, but Cheryl also does not know Charlie’s birthday.”
Cheryl says, “Yes, and Albert still has not figured out Charlie’s birthday.”
Bernard then replies, “Well, now I know his birthday.”
At this point, Albert says, “Yes, we all know it now.”
What is Charlie’s birthday?
Sliding Dominoes
The squares of a 9×9 board are colored as shown, and then its surface is covered with 40 dominoes. Each domino covers two orthogonally adjacent squares, and the uncovered square is a black square on the boundary.
A move shifts a domino along its length by one square, so that it covers one empty square and exposes another. Prove that, for each of the black squares on the board, there’s a sequence of moves that will uncover it.
Words and Numbers
Andrzej Bartz offered these “doubly true” alphametics in the May 2017 issue of Word Ways. If the letters in each equation encode digits, what mathematical facts do these expressions represent?
CCCLVI + CCCI + CCLI = CMVIII
ONE + THIRTYNINE + NINETYONE = THREE + NINE + THIRTY + EIGHTYNINE
TWO × TWO + TEN × FIVE = SIX × NINE
In a Word
anfractuous
adj. having many windings and turnings
loof
n. the palm of the hand
penetralia
n. the innermost recesses of a building
swither
n. a state of perplexity
It’s commonly said that you can defeat a hedge maze by placing one hand on a wall and carefully maintaining that contact as you advance. If the hedges are all connected, this method will reliably lead you to the center of the maze (and, indeed, to every other part of it before you return to the entrance).
The Chevening maze, in Kent, was designed deliberately to thwart this technique. Its center is concealed in an “island” of hedges distinct from the outer wall, so following either a left- or a right-hand rule will return you to the entrance without ever passing the goal.