“People are usually more firmly convinced that their opinions are precious than that they are true.” — George Santayana

“The Cavalry Skirmish”

the cavalry skirmish

This puzzle, by Les Marvin and Sherry Nolan, appeared in the Journal of Recreational Mathematics in 1977. “White to play in the adjoining diagram. If both players play optimally, will White win, lose, or draw?”

I don’t believe JRM ever published the solution. My stab: Either king is vulnerable to a check from the bishop file, and White will win a straight race. So I think Black must play defense. But if White attacks c7 with both knights and Black defends it doubly, then White can simply trade off all four knights (1. Nc7+ Nxc7 2. Nxc7+ Nxc7 bxc7) and the pawn will queen. So I think White wins.

This isn’t a very “mathematical” solution, but I can’t find a reliable alternative involving the parity of the knights’ moves, which seems to be what’s expected. Any ideas?

06/06/2014 UPDATE: A reader ran this position through a couple of strong chess engines and finds that it’s likely a draw — here’s one example:

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[FEN "k6n/Pp4n1/1P6/8/8/6p1/1N4Pp/N6K w - - 0 1"]

1.Nd1 Nf7 2.Nc2 Ne5 3.Nce3 Nd7 4.Nd5 Nxb6 5.Nxb6+ Kxa7 6.Nc8+ Ka6 7.Ne3 b5 8.Nd6 b4 9.Ne4 Nh5 10.Nc2 Kb5 11.Nxb4 Kxb4 12.Nxg3 Nxg3+ 13.Kxh2 Nf1+ 14.Kh3 Ne3 15.g4 Kb3 16.g5 Nd5 17.g6 Nf4+ 18.Kg3 Nxg6

There doesn’t seem to be a sure way for either side to reach a win. I suspect that Marvin and Nolan thought otherwise, but they were writing in 1977, without the benefit of computer analysis. Without a published solution, we can’t be sure.

(Thanks, Emilio.)

A Lasting Gift


Letter from Richard Byrd to his son shortly after establishing Marie Byrd Land, Feb. 22, 1929:

Dear Dickie–

I have named a big new land after mommie because mommie is the sweetest finest and nicest and best person in the world. Take good care of her and be awfully sweet to her while I’m away.

I love you my dear boy.

Little America

Love and Gold


An amorous M.A.
Says that Cupid, the C.D.,
Doesn’t cast for his health
But is rolling in wealth —
He’s the John Jaco-B.H.

— Anonymous

Give and Take


The rocky island of Märket lies in the Baltic Sea between Sweden and Finland. When the Finns put a lighthouse on it in 1885, they unwittingly put it on Swedish territory.

This created a problem: Without moving the lighthouse or altering the coastline, the parties had to find a way to reapportion the island equitably according to their agreement.

The solution was to draw a reverse S on the map: Sweden grants Finland the lighthouse, but it gains a corresponding incursion into Finnish territory, so the island’s balance is restored.

It must be tricky to play croquet, though.

Somewhat related: The Tehachapi Loop.

The Ghost Plane

On Dec. 8, 1942, American forces in Kienow, China, spotted an unidentified plane heading toward them on a beeline from Formosa. Pilots Bob Scott and Johnny Hampshire approached it and discovered it was an old American P-40B Tomahawk bearing an insignia that hadn’t been seen since Pearl Harbor. The pilot would not identify himself.

Fearing a trick by the Japanese, Scott and Hampshire fired briefly on the plane, but it sought neither to evade them nor to counterattack. Scott moved to the plane’s farther side and saw that it had been badly damaged before they came upon it — the canopy had been shot away, the right aileron was gone, and part of the wing was missing. The pilot’s head was slumped on his chest. Strangest of all, the P-40B had no landing gear — the wheel wells were empty.

Scott and Hampshire lost the plane in a cloud bank and then saw it crash in a rice paddy below. Who was the pilot, and where had the strange plane come from? No one knows, but after years of research Scott evolved a conjecture that it had been assembled by a small group of Air Corps personnel who had retreated from Bataan to Corregidor and then to Mindanao. If this is true it must have flown more than 1,000 miles through enemy airspace to reach China.

Japanese records confirm that there was an American P-40 over Formosa on Dec. 8, 1942, but where it came from, where it was headed, and indeed how it even got airborne remain a mystery.

In a Word

n. the condition of being left-handed

The Hairy Ball Theorem


A hairy ball can’t be combed flat — it must always have a cowlick.

This result arose originally in algebraic topology, but it has intriguing applications elsewhere. For example, it can’t be windy everywhere at once on Earth’s surface — at any given moment, the horizontal wind speed somewhere must be zero.


These have been in my notes for years — I can’t conclusively disprove them, but I have my doubts:

  • In 1930 four Germans bailed out of a glider inside a thundercloud over the Rhön Mountains, were carried upward by their parachutes into a region of supercooled vapor, and froze to death.
  • The monument to Jose Olmedo in Guyaquil, Ecuador, is actually a secondhand statue of Lord Byron, substituted because the town had no money. (Also: Cuzco, Peru, is rumored to have a statue of Chief Powhatan rather than Atahualpa.)
  • A surprising number of sources claim that Mississippi spent a fifth of its revenues on artificial limbs in 1866.
  • In 1902 Germany manufactured a “Goethemobile” in honor of the poet. (I really hope this is true.)

Debunk/rebunk/semi-unbunk as you please.

Catching Rays

In 1984, Bob Ellis, managing editor of the Eldorado, Ill., Daily Journal, announced a contest “to recognize and honor the American summer tradition, Daylight Saving Time.”

“The rules are simple,” Ellis wrote. “Beginning with the first day of Daylight Savings Time this year, those entering the contest must begin saving daylight. Whoever saves the most daylight … will be awarded prizes.”

He arranged for the contest to end on April 1, and hoped he had inserted enough absurdities that readers would see the joke. No pre-dawn light or twilight would be accepted, and moonlight was disallowed. Contestants could store their light in any container and deliver it to the Journal’s office. “All entries will be donated to less fortunate nations that do not observe Daylight Saving Time.”

But they didn’t. Ellis was contacted by media in San Francisco, New York, Chicago, Dallas, “every section of the nation” seeking more information about the contest.

That was all right with Ellis. He’s written the piece as “change of pace from the usual and often gloomy side of the news,” he said, so that people “could laugh at the world, and me, and perhaps even at themselves, with reckless abandon. And feel good. And therein lies the worth of such a diversion.”