CyberChance

A puzzle by National Security Agency applied research mathematician Nicholas R., from the agency’s October 2016 Puzzle Periodical:

Eddie, Layne, Kurt, and Chris are locked in a heated game of CyberChance which only one of them will win. Their fans are on the edge of their seats: everyone knows that in CyberChance, things can change at any moment. One fan, who prefers Kurt or Chris, is feeling worried since there is only a 4-in-10 chance that one of them will win. An Eddie fan brags that Eddie is twice as likely as Layne to come out on top. Another Eddie fan concurs, and adds the following observation: Chris is Eddie’s main competition. He figures that, given that Chris doesn’t win, Eddie has a 4-in-7 chance of winning. A Kurt fan has been quietly standing in the corner, listening to all the other fans, and wonders: What chance does Kurt have of winning CyberChance?

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| Puzzles

Polchinski’s Paradox

https://commons.wikimedia.org/wiki/File:Grandfather_paradox_billiard_ball.svg
Image: Wikimedia Commons

In 1990, physicist Joseph Polchinski described a puzzling situation: Suppose a billiard ball were sent through a traversable wormhole into the past, where it knocked its earlier self off course, away from the wormhole. This is a version of the famous grandfather paradox: How can we explain the ball’s presence where it seems to have prevented its own arrival?

Fortunately, Caltech students Fernando Echeverria and Gunnar Klinkhammer found that self-consistent solutions exist in which the older ball imparts only a glancing blow to its younger self, one that sends it through the hole at just the right angle to deliver a similarly glancing blow to its own forebear, and so on, sparing us from the paradox. (In 1991 the students and Kip Thorne reported that they’d failed to find any initial conditions in which such self-consistent solutions were unavailable, so it’s plausible that they exist for every possible initial trajectory. But this hasn’t been proven.)

Another pleasing possibility is that the older ball knocks the younger out of the way and itself enters the wormhole again. This creates an infinite loop, and some existential bewilderment, but no paradox.

| Oddities · Science & Math

Tile Swap

You’re tiling a floor with 4×1 and 2×2 tiles when you accidentally break one. A tile of the other shape is available. Show that it’s not possible to cover the floor by rearranging the tiles.

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| Puzzles

Black and White

khanyan chess puzzle

Alexey Khanyan devised this “no-brainer” in 2008. Black is in check. His only legal response is to interpose one of his knights, which then checks White, who must capture the knight, and so on. The whole ensuing 22-ply bloodbath unfolds mechanically, always reaching the same conclusion.

Via Tim Krabbé’s chess diary. Krabbé writes, “As it is a no-brainer, I feel free not to give the moves.” See The Sure Thing.

| Puzzles

Postal Inspector

In 1897, to help inaugurate New York City’s new pneumatic mail system, officials sent a live black cat in a canister from the Produce Exchange Post Office on Bowling Green to the General Post Office on Park Row, a distance of 3,750 feet.

“How it could live after being shot at terrific speed from Station P in the Produce Exchange Building, making several turns before reaching Broadway and Park Row, I cannot conceive, but it did,” recalled postal supervisor Howard Wallace Connelly. “It seemed to be dazed for a minute or two but started to run and was quickly secured and placed in a basket that had been provided for that purpose.”

At its peak the system would carry 95,000 letters a day through 27 miles of tubes connecting 23 post offices. It was discontinued in 1953, outmoded by the growing volume of mail and the advent of the automobile.

| Oddities · Technology

Nothing Doing

Recess, County Galway, Ireland:

https://commons.wikimedia.org/wiki/File:Monument_to_nothing,_Recess_-_geograph.org.uk_-_381638.jpg
Image: Wikimedia Commons

Aspelt, Luxembourg:

https://commons.wikimedia.org/wiki/File:Aspelt_Plaque_Nothing_happened.jpg
Image: Wikimedia Commons

Bechyne, Czech Republic:

https://commons.wikimedia.org/wiki/File:Bechyn%C4%9B,_Z%C3%A1%C5%99e%C4%8D%C3%AD_481,_zde_v_tomto_dom%C4%9B.jpg
Image: Wikimedia Commons

(“In this house, no important person was born, lived, and most importantly did not die, and that is why we live well here.”)

Záblatí-Hlásná Lhota, Czech Republic:

https://commons.wikimedia.org/wiki/File:Hl%C3%A1sn%C3%A1_Lhota_(Z%C3%A1blat%C3%AD)_07.jpg
Image: Wikimedia Commons

(“Hlásná Lhota – a stone in whose surroundings nothing significant has demonstrably happened for several hundred years”)

Míšov, Czech Republic:

https://commons.wikimedia.org/wiki/File:M%C3%AD%C5%A1ov_-_Cimrman.jpg
Image: Wikimedia Commons

(“On 8 May 1915 in Míšov, the great Czech genius Jára Cimrman just barely missed being involved in something historically important.”)

O’Hungry’s Café, Old Town San Diego State Historic Park:

https://commons.wikimedia.org/wiki/File:On_This_Site_in_1897_Nothing_Happened_-_Sign_in_O%27Hungry%27s_Cafe_-_San_Diego_State_Historic_Park_-_San_Diego,_CA_-_USA_(6930668317).jpg
Image: Wikimedia Commons

York, Western Australia:

https://commons.wikimedia.org/wiki/File:On_this_site_in_1897_nothing_happened_(4525842700).jpg
Image: Wikimedia Commons

Villa de Leyva, Boyacá Department, Colombia:

https://commons.wikimedia.org/wiki/File:Villa_de_Leyva,_Colombia_02.jpg

(“On October 13, 1825, nothing happened in this house, nor was anyone important born.”)

| Humor · Oddities

Friendly Numbers

The divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Add those up and divide the sum by 30 itself and you get 12/5.

The divisors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. Add those up and divide the sum by 140 and you also get 12/5.

This makes 30 and 140 a friendly pair. Other members of their little club are 2480, 6200, and 40640.

Interestingly, no one knows whether 10 has such a partner. If it does, its smallest friend is at least 1030.

| Science & Math

In a Word

intendiment
n. intention or purpose

auspicate
v. to begin an undertaking

mercation
n. the act of purchasing something

Alnaschar
n. a person given to unrealistic dreams, expectations, or plans

In the summer of 1967, the Beatles briefly considered buying a set of Greek islands where they could live and work together.

“We were all going to live together now, in a huge estate,” Derek Taylor says in Anthology. “The four Beatles and Brian [Epstein] would have their network at the centre of the compound: a dome of glass and iron tracery (not unlike the old Crystal Palace) above the mutual creative/play area, from which arbours and avenues would lead off like spokes from a wheel to the four vast and incredibly beautiful separate living units. In the outer grounds, the houses of the inner clique: Neil [Aspinall], Mal [Evans], Terry [Doran] and Derek, complete with partners, families and friends.”

John, Paul, and George got as far as touring the islands south of Athens and visiting one they considered buying. But indulging the idea for an afternoon seemed to be enough for them. George said, “We got back on the boat and sailed away, and never thought about the island again.”

“It’s a good job we didn’t do it,” Paul said later, “because anyone who tried those ideas realised eventually there would always be arguments, there would always be who has to do the washing-up and whose turn it is to clean out the latrines. I don’t think any of us were thinking of that.”

| Entertainment · Language