Unlimited Shuffleboard


Jules Verne’s 1895 novel Propeller Island imagines an immense ship in the Pacific Ocean that’s inhabited entirely by millionaires. In 1999 an organization calling itself Freedom Ship International proposed the real thing, a ship four times as long as the Queen Mary and 25 stories tall. Altogether the ship would boast 18,000 living units, 3,000 commercial units, 2,400 time-share units and 10,000 hotel units, and like Verne’s ship it would circle the world continuously.

“The proposed vessel’s superstructure, rising twenty-five stories above its broad main deck, would house residential space, a library, schools, and a first-class hospital in addition to retail and wholesale shops, banks, hotels, restaurants, entertainment facilities, casinos, offices, warehouses, and light manufacturing and assembly enterprises.”

Cost estimates started at $6 billion but soon nearly doubled, and construction still hasn’t begun, though the company was actively pursuing its plans as recently as November 2013. While you’re waiting, you can stay on this giant yacht.

Math Notes

(15 + 25) + (17 + 27) = 2 (1 + 2)4

(15 + 25 + 35) + (17 + 27 + 37) = 2 (1 + 2 + 3)4

(15 + 25 + 35 + 45) + (17 + 27 + 37 + 47) = 2 (1 + 2 + 3 + 4)4

(15 + 25 + 35 + 45 + 55) + (17 + 27 + 37 + 47 + 57) = 2 (1 + 2 + 3 + 4 + 5)4

Life Size


Human-scale chess has been played for centuries — the Italian town of Marostica has staged a game every two years since 1923, and the photo above shows actual soldiers (and cannon!) in a game in St. Petersburg in 1924.

In 2003 Sharilyn Neidhardt organized a game on a board represented by 64 city blocks on the Lower East Side of New York. Two expert players played the game on an ordinary board at the ABC No Rio gallery, in the middle of the street grid. Each time one of them made a move, the corresponding piece received a call or a text message (“go to f7”) and had to travel to the corresponding square, on foot or by bike or roller skate. If you were captured you became an ordinary person again.

Players were recruited online; each had to have a working cell phone, “be excruciatingly on time,” and be willing to spend about three hours awaiting orders. Neidhardt warned newcomers: center pawns can expect to be captured early, bishops and knights will cover a lot of territory, and kings will have a low-key opening and a busy endgame.

As of 2014, eight games had been played, in New York, San Francisco, Vancouver, and Austin. Here’s a knight’s diary of the New York game.

(From Karen O’Rourke, Walking and Mapping, 2013.)

Travel Planning


In 1794 a penurious Sydney Smith accepted an offer to spend the holidays with some friends in Gloucestershire.

“Your offer of a horse to carry my portmanteau I cannot accept, and for two reasons, which I think will justify me in not accepting it,” he wrote. “The first is, you have no horse here; the next, I have no portmanteau.”

The Angel Problem

Image: Wikimedia Commons

An angel stands on an infinite chessboard. On each turn she can move at most 3 king’s moves from her current position. Play then passes to a devil, who can eat any square on the board. The angel can’t land on an eaten square, but she can fly over it, as angels have wings. (In the diagram above, the angel starts at the origin of the grid and, since she’s limited to 3 king’s moves, can’t pass beyond the blue dotted boundary on her next turn.)

The devil wins if he can strand the angel by surrounding her with a “moat” 3 squares wide. The angel wins if she can continue to move forever. Who will succeed?

John Conway, who posed this question in 1982, offered $100 for a winning strategy for an angel of sufficiently high “power” (3 moves may not be enough; in fact a 1-power angel, an actual chess king, will lose). He also offered $1000 for a strategy that will enable a devil to win against an angel of any power.

It’s not immediately clear what strategy can save the angel. If she simply flees from nearby eaten squares, the devil can build a giant horseshoe and drive her into it. If she sprints in a single direction, the devil can build an impenetrable wall to stop her.

In fact it wasn’t until 2006 that András Máthé and Oddvar Kloster both showed that the angel has a winning strategy. In some variants, in higher dimensions, it’s still not certain she can survive.

(John H. Conway, “The Angel Problem,” in Richard J. Nowakowski, ed., Games of No Chance, 1996.)

While You Wait


Old Faithful is sometimes degraded by being made a laundry. Garments placed in the crater during quiescence are ejected thoroughly washed when the eruption takes place. Gen. Sheridan’s men, in 1882, found that linen and cotton fabrics were uninjured by the action of the water, but woolen clothes were torn to shreds.

— William C. Riley, Official Guide to the Yellowstone National Park, 1889



How can an umpire be sure a runner has reached first base? In 1875 inventor John O’Neill suggested fitting it with a bell to “indicate clearly and positively, without chance of error, the exact moment when the base is touched by the runner.”

The trouble is that the “enunciating base” will also sound when the first baseman steps on it. Ten years later William Williams suggested an electric bell, which could be heard more clearly by a single umpire behind home plate, but it faced the same objection. Both were forgotten.



Artist Markus Raetz erected this sign on the Rue du Rhône (at Place de la Fusterie) in downtown Geneva. What it says depends on where you stand.

Here’s a similar idea exhibited in a gallery:


Each year, thousands of people take up seats along the streets of Flanders. Before each of them is a wooden box, and in each box is a single male finch. At a timekeeper’s signal, the observers begin to count the birds’ calls, making tally marks on long wooden sticks. After one hour, the bird that has sung the most calls is recognized as the winner.

This is vinkensport, a tradition in Flemish culture for more than 400 years. It was started by merchants in 1596, and as of 2007 an estimated 13,000 vinkeniers were still breeding 10,000 birds each year.

The sport’s popularity is growing, but like any sport it’s subject to cheating: When one finch produced 1,278 susk-e-wiets in an hour, its owner was accused of doping it with testosterone. Another competitor attracted suspicion when his box emitted exactly 725 calls in each of two matches; when a judge ordered the box opened, he discovered a mini-CD player inside.