# Leapfrog

A puzzle by Y. Ionin, from the September/October 1990 issue of Quantum:

Three frogs occupy three vertices of a square. When one frog jumps over another, it lands beyond it at the same distance that had originally separated them. Can any frog reach the fourth vertex?

# All Right

In a French journal Oscar Wilde once saw the drawing of a bonnet.

Under it were the words “With this style the mouth is worn slightly open.”

# Javelin

A puzzle by Steven T., a systems engineer at the National Security Agency, from the NSA’s September 2016 Puzzle Periodical:

Three athletes (and only three athletes) participate in a series of track and field events. Points are awarded for 1st, 2nd, and 3rd place in each event (the same points for each event, i.e. 1st always gets “x” points, 2nd always gets “y” points, 3rd always gets “z” points), with x > y > z > 0, and all point values being integers.

The athletes are named Adam, Bob, and Charlie.

• Adam finished first overall with 22 points.
• Bob won the Javelin event and finished with 9 points overall.
• Charlie also finished with 9 points overall.

Question: Who finished second in the 100-meter dash (and why)?

# Spotted

In a 1963 issue of Bokmakierie, a magazine for birdwatchers, Frank A. Goodliffe described a curiously familiar species he called Clericus polydenominata, the “dog-collared sombre blackbird”:

Identification: Similar to common laity but plumage and behaviour should serve to differentiate. Plumage black with narrow white collar — unbroken at throat. Feet black, of leathery appearance. Beak pink — often with blueish tint during winter months. When in groups are often seen with wings folded behind rump. … Habits: Usually found congregating with flocks of common laity, the females of which are frequently seen with plumage of vivid colours. Nesting: This usually occurs close to old buildings with spires. They are usually very friendly and may be seen around nesting sites of common laity at tea-time. … Call: The voice is distinctive, commencing ‘Brrrrr–rethren’ and continuing low and pleasant — often prolonged. Usually sings in congregations.

In a private booklet published four years later, M.A. Traylor suggested that the species belonged in the family of bishop birds.

# Unquote

“How happy many people would be if they cared about other people’s affairs as little as about their own.” — G.C. Lichtenberg

“Most people enjoy the inferiority of their best friends.” — Lord Chesterfield

“We all have strength enough to endure the misfortunes of others.” — La Rochefoucauld

“I set it down as a fact that if all men knew what each said of the other, there would not be four friends in the world.” — Pascal

# No Play Zone

In an April 3, 1971, letter to the editor of the Saturday Review, reader K. Jason Sitewell reported some alarming news: A congressman named A.F. Day had introduced a bill that would abolish all private parks of more than 50 acres and all public recreation areas that were used by fewer than 150 people a day. The practical effect would be to abolish the nation’s golf courses.

Sitewell said he understood Day’s motive because he’d grown up with him. The congressman’s grandfather had “perished in a sand trap,” and his father had died of a coronary after hitting 19 balls into a pond.

An uproar followed. Country clubs vowed to fight the bill, constituents besieged their representatives, and editorials decried the measure, which Golf World called “as ominous a threat to golf as anything that has come along.”

But eventually it became clear that there was no such bill and readers saw the link between the purported congressman’s name and the date of Sitewell’s letter. It turned out that the whole thing had been a jape cooked up by Review editor and inveterate prankster Norman Cousins.

“I wrote apologies to each subscriber who had been offended or angered,” Cousins wrote. “I begged my golfing friends, who threatened to have me barred from every course in the nation, to forgive me for my joke. I suffered enough every time I played, I told them, and penance was awaiting me on each tee.”

# A Polyhex Square

From Lee Sallows:

(Thanks, Lee!)

# Kinship

That is a simple rule, and easy to remember. When I, a thoughtful and unblessed Presbyterian, examine the Koran, I know that beyond any question every Mohammedan is insane; not in all things, but in religious matters. When a thoughtful and unblessed Mohammedan examines the Westminster Catechism, he knows that beyond any question I am spiritually insane. I cannot prove to him that he is insane, because you never can prove anything to a lunatic — for that is a part of his insanity and the evidence of it. He cannot prove to me that I am insane, for my mind has the same defect that afflicts his. All Democrats are insane, but not one of them knows it; none but the Republicans and Mugwumps know it. All the Republicans are insane, but only the Democrats and Mugwumps can perceive it. The rule is perfect: in all matters of opinion our adversaries are insane.

— Mark Twain, Christian Science, 1907

# Amalgamation

Putting mercury in contact with an aluminum plate has some surprising consequences (2:05).

# Endless Love

Joe invents a time machine. He travels back in time and meets Emily, and they have a child, Bill. Bill grows up, meets Carol, and has a child, Joe. Joe grows up and invents a time machine, and so on.

Joe and Bill are each the other’s father and son, and each man is his own grandfather.

From Dave Morice’s Alphabet Avenue, 1997. See “Proof That a Man Can Be His Own Grandfather” and Oedipus Wrecked. Robert Heinlein’s 1959 story “‘–All You Zombies–‘” is even more confusing.