Round Numbers

Alan and Bob are playing a game of marbles. Alan has two marbles, Bob has one, and each rolls to try to come nearest to a fixed point. If the two have equal skill, what is the chance that Alan will win?

There seem to be two contradictory arguments. On the one hand, each of the three marbles has an equal chance of winning, and two of them belong to Alan, so it seems that there’s a 2/3 chance that Alan will win.

On the other hand, there are four possible outcomes: (a) both of Alan’s rolls are better than Bob’s, (b) Alan’s first roll is better than Bob’s, but his second is worse, (c) Alan’s first roll is worse than Bob’s, but his second is better, and (d) both of Alan’s rolls are worse than Bob’s. In 3 of the 4 cases, Alan wins, so it appears that his overall chance of winning is 3/4.

Which argument is correct?

Click for Answer

Presidential Timber

In 1940 Ronald Reagan was voted a “Twentieth Century Adonis” by the University of Southern California’s Division of Fine Arts for having the “most nearly perfect male figure.”

He posed for student sculptors there.


Twenty-nine-year-old James Landis was operating a currency-wrapping machine at the U.S. Bureau of Engraving and Printing when an idea occurred to him. He went home and cut ordinary bond paper into pieces the size of U.S. currency, and wrapped them to resemble the bricks of $20 bills that he produced at work. On Dec. 30, 1953, he smuggled these packages into work with him and hid them in a locker room. Then he wrapped two bundles of real $20 bills in kraft paper and carried them to a storage area. There he unwrapped them, saving the labels, put the bills into two paper bags he had brought from home, and hid these.

He worked the rest of the morning at his station, then returned to the dummy bundles he had brought from home. In a toilet stall he affixed the labels to the ends of the dummy bricks, using glue he had brought from his station, and he rubber-stamped each “HA 12-31-53,” indicating that a bureau employee with the initials H.A. had wrapped the packages on Dec. 31, 1953. Then he carried the dummy bricks to a storage skid on the first floor, where he left them among packages of genuine $20 bills.

At 3:10 p.m. he finished work, changed clothes, and retrieved one of the paper bags from the dead storage area, using a pair of dirty trousers to conceal the $128,000 that the bag held. And he walked out of the building.

Landis and three friends set about buying inexpensive merchandise in order to shed the stolen money and get change, but it wasn’t to last long. When he returned to work on Jan. 4, a stockman picked up two bricks of currency and noted that one of them felt light. When the dummy bricks were discovered, the Secret Service began an investigation; Landis drove to Virginia and tried to hide the money with his father-in-law, who turned him in the following morning. Landis and his friends pleaded guilty on May 3, and all were sent to prison.

Good Enough

Ixonia, Wisconsin, was named at random.

Unable to agree on a name for the town, the residents printed the alphabet on slips of paper, and a girl named Mary Piper drew letters successively until a name was formed.

The town was christened Ixonia on Jan. 21, 1846, and it remains the only Ixonia in the United States.

More Is Less

A riddle attributed to British prime minister George Canning, among many others:

A word there is of plural number,
Foe to ease and tranquil slumber.
Any other word you take
And add an S will plural make;
But if you add an S to this,
So strange the metamorphosis,
Plural is plural now no more
And sweet what bitter was before.

Click for Answer


Astronaut John Young smuggled a corned beef sandwich into space. As Gemini 3 was circling Earth in March 1965, Young pulled the sandwich out of his pocket and offered it to Gus Grissom:

Grissom: What is it?

Young: Corned beef sandwich.

Grissom: Where did that come from?

Young: I brought it with me. Let’s see how it tastes. Smells, doesn’t it?

Grissom: Yes, it’s breaking up. I’m going to stick it in my pocket.

Young: Is it? It was a thought, anyway.

“Wally Schirra had the sandwich made up at a restaurant at Cocoa Beach a couple of days before, and I hid it in a pocket of my space suit,” Young explained later. “Gus had been bored by the official menus we’d practiced with in training, and it seemed like a fun idea at the time.”

Grissom wrote, “After the flight our superiors at NASA let us know in no uncertain terms that non-man-rated corned beef sandwiches were out for future space missions. But John’s deadpan offer of this strictly non-regulation goodie remains one of the highlights of our flight for me.”


“The greatest masterpiece in literature is only a dictionary out of order.” — Jean Cocteau

To Do

Titles of actual publications collected by librarian Eric v.d. Luft:

How to Abandon Ship (1942)
How to Abduct a Highland Lord (2007)
How to Attract the Wombat (1949)
How to Avoid Intercourse With Your Unfriendly Car Mechanic (1977)
How to Be an Ocean Scientist in Your Own Home (1988)
How to Become Extinct (1941)
How to Boil Water (1976)
How to Break Out of Prison (2003)
How to Bribe a Judge (2002)
How to Buy an Elephant (1977)
How to Deep-Freeze a Mammoth (1986)
How to Dig a Hole to the Other Side of the World (1979)
How to Embalm Your Mother-in-Law (1993)
How to Get a Gorilla Out of Your Bathtub (2006)
How to Hold a Crocodile (1981)
How to Label a Goat (2006)
How to Ride a Tiger (1983)
How to Run a Bassoon Factory (1934)
How to Tell a Blackbird From a Sausage (2007)
How to Tell If Your Boyfriend Is the Antichrist (2007)
How to Travel With a Salmon (1994)
How to Trick or Treat in Outer Space (2004)
How to Wreck a Building (1982)

The list was begun by librarians at Bowdoin College in the 1970s; Luft inherited it there and has maintained it ever since. He published a selection in 2008 as The Inscribed List: Or Why Librarians Are Crazy. “We librarians don’t go deliberately looking for these little nuggets of delight,” he writes. “We don’t have to. They just appear.”

The Mere Addition Paradox

From Derek Parfit’s Reasons and Persons: World A contains a large group of people (say, 10 billion), all of whom have a high level of happiness. The width of the bar represents the size of the group, and its height represents their happiness.

World A+ contains twice as many people — the original group, plus a second group who are worse off. Assuming their lives are still happy, though, it appears that A+ is no worse than A. (Assume that the groups don’t know of one another, so there is no social injustice.)

In B-, the two groups are still distinct and of equal size, but all the inhabitants are somewhat happier than the average level in A+ — say, four-fifths the level in A.

Now combine the groups to produce B. This seems as good as B-, since we’ve only merged the two populations.

Intuitively, many people would feel that World B is worse than World A — all its inhabitants are less happy. But the logic seems to indicate that B is better — that “merely adding” people with tolerably happy lives makes the world a better place. Does it?

Double Play

This Latin sentence consists entirely of repeated syllables:

Te tero, Roma, manu nuda, date tela, latete.

“It is you I destroy, Rome, with bare hands, give up weapons, hide yourself.”

See Repeat Performance.