In 1775, an enciphered message was intercepted en route from colonial physician Benjamin Church to a British officer in Boston. Part of the message appears below. What does it say?

# Puzzles

# Black and White

Physicist Roger Penrose devised this problem in 2017 to illustrate the difference between artificial and human intelligence. James Tagg, leader of the Penrose Institute, told the *Telegraph*, “A human looking at it for a short while will ‘see’ what white must, and more particularly, must not do, and use very little energy to decide this. But, for a computer, the puzzle requires an enormous number of calculations, far too many for even today’s supercomputers.” What is White’s insight?

# Euphony

A charming puzzle from *Crux Mathematicorum*, December 2004:

If all plinks are plonks and some plunks are plinks, which of these statements must be true?

X: All plinks are plunks.

Y: Some plonks are plunks.

Z: Some plinks are not plunks.

# Podcast Episode 317: Lateral Thinking Puzzles

Here are six new lateral thinking puzzles — play along with us as we try to untangle some perplexing situations using yes-or-no questions.

# Board Meeting

Prove that if seven darts land on a dartboard, there will always be two darts that are no farther apart than the distance of one radius.

# Black and White

Black is clearly lost. But there are two squares on which his king can never be checkmated, even if White is allowed to make consecutive moves and checks are ignored. What are they?

# Pursuit

A problem from Sam Loyd’s *Cyclopedia of Puzzles*, 1914:

Here is the puzzle of Tom the Piper’s Son, who, as told by ‘Mother Goose,’ stole the pig and away he run. It is known that Tom entered the far gate shown at the top on the right hand. The pig was rooting at the base of the tree 250 yards distant, and Tom captured it by always running directly towards it, while the pig made a bee-line towards the lower corner as shown. Now, assuming that Tom ran one-third faster than the pig, how far did the pig run before he was caught?

Intriguingly, Loyd adds, “The puzzle is a remarkable one on account of its apparent simplicity and yet the ordinary manner of handling problems of this character is so complicated that solvers are asked merely to submit approximately correct answers, based upon judgment and common sense, just to see who can make the best guess. The simple rule for solving it, however, which will doubtless be quite new to our puzzlists, is based upon elementary arithmetic.” What’s the answer?

# Black and White

In 1915 James Ferguson Smyth invited Hermann Helms to play a practice game at the Manhattan Chess Club. They had reached the position above when Helms, as Black, found a brilliant two-move mate. What is it?

# Red Square

A problem from the 1999 Russian Mathematical Olympiad:

Each cell of a 50×50 square is colored in one of four colors. Show that there exists a square which has cells of the same color as it directly above, directly below, directly to the left, and directly to the right of it (though not necessarily adjacent to it).

# A Perfect Square

An old problem from the Soviet Mathematical Olympiad:

Find the 4-digit number *aabb* that is a perfect square.