Sunday, November 14, 2010

040 - Greenjack

Some time ago, Farmer Joe made the mistake of gambling against one of his regular customers.

The game was Greenjack, a popular betting game in Serendipity. It is played with a deck of only 16 cards, divided into four suits: Red, Blue, Orange, and Green. There are four cards in each suit: Ace, King, Queen and Jack. Ace outranks King, which outranks Queen, which outranks Jack - except for the Green Jack, which outranks every other card.

If two cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green, again except for the Green Jack, which outranks everything.

Farmer Joe, who is not the dealer, is dealt a card face up which both players can see. The dealer deals themselves a card, which they look at and then place face down. The dealer then makes three true statements which are capable of identifying which card is higher. If Farmer Joe correctly identifies which card is higher from the statements, he wins; otherwise he loses.

On this occasion, Farmer Joe was dealt the Blue King.

The dealer said:

1) My card would beat a Green King.
2) Knowing this, if my card is more likely to be a Jack than a Queen, then my card is a King. Otherwise, it isn't.
3) Given all of the information that you now know, if my card is more likely to beat yours than not, then my card is Red. Otherwise it isn't.

Farmer Joe got it wrong and lost the bet. Can you do better? Who holds the higher card?

Thursday, November 11, 2010

039 - The Devil's Dice

Zephyr Cantrell possesses an unusual set of six-sided dice.

There are four dice in total. The faces of the dice each bear an integer between 1 and 24 inclusive. Each integer is used and none are repeated. Each of the dice has a different colour. The dice are perfectly weighted and each face of each die has an exactly 1 in 6 chance of being rolled.

The red die rolls a higher number than the blue die more often than not.
The blue die rolls a higher number than the green die more often than not.
The green die rolls a higher number than the yellow die more often that not.
The yellow die rolls a higher number than the red die more often than not.
The number 14 appears on the red die.

How are the faces of the dice numbered?

Wednesday, November 10, 2010

038 - Mornington Crescent

I was lucky enough while idling at Serendipity University today to witness an masterclass in the game of Mornington Crescent between Zephyr Cantrell and Urtha Bennett. Naturally you're well aware of the rules, but until you've seen it played by intellects of this calibre you've never really seen it played.

After the traditional round of drafting, and a clarification that yes, they were playing the Lyttleton variant, Zephyr opened with a Dutch runabout to Moorgate via Aldgate East, which personally I've never seen played before, and apparently neither had the rest of the audience, judging by the gasps. Equally surprising was Urtha countering with a fourfold blind through Euston/Warren/Goodge.

From there the two played a cat-and-mouse game across the Hammersmith & City line, with the highpoints being a Layman's Knee by Zephyr at Sudbury Town (with Egyptian Cross to Golders Green, no less), and an even more impressive triple crown for Urtha culminating at Blackfriars. This, mind you, after being scuttled at Baker Street, Knightsbridge and Shepherd's Bush - in that order!

However, all good things must come to an end, and on her eleventh turn Zephyr made the mistake of passing west at Paddington to avoid a Southwark/Putney Bridge pin without noticing the worrying state of the Embankment. Seizing the moment, Urtha dove in to make the final move and win the game.

What was Urtha's game-winning play?

Tuesday, November 9, 2010

037 - The Journey of Abernathy Gould

"Let me tell you a story," says Jacki Renquist as she leads Kent Dockland through the Logidyne Labs complex. "This happened during my grandfather's time."

"The great explorer, Abernathy Gould, came to western edge of a vast desert. She had with her her eight stalwart companions. Each of the nine travellers was driving an all-terrain car capable of travelling forty miles to the gallon - which was also the capacity of their cars' petrol tanks."

"When they reached the western edge of the desert, every car had a full tank of petrol, and each car carried nine extra gallon tins of petrol (that being the largest number of tins a single car was capable of carrying)."

"Under Gould's leadership, the nine travellers set out in a straight line east across the desert with the aim of Gould travelling the furthest distance east that she could manage, in the hope of finding.... something. All nine travellers returned safely, along with their cars, to the western edge of the desert at the conclusion of the journey. No additional petrol was acquired during the journey, no petrol was left unattended in the desert for any length of time (or, for that matter, with a car or driver to guard it), and none of the explorers travelled any distance on foot (as a journey on foot through the desert was said to spell certain death)."

"Gould later claimed that the distance she travelled into the desert was the greatest distance she could have achieved under the circumstances - which is lucky, as she only barely found what she was looking for."

Assuming Gould's claim is correct, how far east did she travel?

Monday, November 8, 2010

036 - What Kind Of Day Has It Been

Anwar Patel poses the following challenge to his students:

"In television, there are few episodes more important than the finale of the first season.  In addition to the normal drive to achieve high ratings, it also needs to compete against other season finales, leave viewers with a strong impression of the show to drive excitement for a second season, and, in the case of shows not lucky enough to be renewed, serve as a satisfying finale for the show's run."

"Can you match the following season 1 finale titles to the correct plotlines?"

1) The Neutral Zone
2) The Erlenmeyer Flask
3) Exodus
4) These Are The Days
5) Honeymoon
6) Fall Out
7) Kobol's Last Gleaming
8) Some Enchanted Evening
9) Sold Under Sin
10) A World Of His Own

a) Smoke is seen and a hatch is opened.
b) A man is killed while handing over a unique baby.
c) A playwright demonstrates unusual powers - including over a famous narrator.
d) Two men want to swap hearts.
e) An escape by six and an unmasking of one.
f) A parade, and a hardware salesman takes a new job.
g) Nine outposts go silent and three frozen travellers are found.
h) A doctor treats his ex-girlfriend's new husband.
i) A woman finds an arrow and a man visits an opera house.
j) Children match wits with an evil babysitter

Sunday, November 7, 2010

035 - Grand Tour

Add lines to this grid so as to make a single closed path that touches every dot.

* Lines must be perfectly vertical or horizontal.

* Lines must begin at a dot and end at a different dot.

* For clarity, "single closed path" means a path forming a single uninterrupted line without beginning or end.

* Your path must include the lines already marked on the grid.

Thursday, November 4, 2010

034 - Rational Pirates

Every morning the children of Serendipity thrill to the television adventures of Cap'n Redhook and his crew of perfectly rational sea-dogs as they sail the high seas in their clockwork ship The Razor of Occam.

Redhook's gang have an unusual way of dividing loot. The eldest pirate (in this case, Redhook) gets to propose a method of sharing the loot, and then all pirates (including the eldest) take a vote.  If a majority of pirates vote against the proposed split, the proposer gets thrown to the sharks, and the new eldest pirate proposes a new split, and so on until a split of loot is accepted.

In today's episode - Attack of the Cybersquid - Cap'n Redhook and his gang have looted 100 pieces o' eight from their nemesis, Admiral Goldbelly.  When it comes time to split the loot, what is the largest number of pieces o' eight Redhook can retain for himself?

Additional information:
* There are five pirates in Redhook's crew, including Redhook.
* All five pirates will vote so as to maximise their personal gain.  None are bothered by feeding their crewmembers to the sharks.
* Pieces o' eight can't be divided into fractions - the number of pieces o' eight each pirate gets must be an integer.
* Tied votes are resolved in favour of the proposer.

Wednesday, November 3, 2010

033 - Diggings

The original inhabitants of Serendipity are the cause of much speculation among archaeologists. Completely vanished by the time of the first European settlers, we only know them through the artifacts and art that they left behind.

The attached image is typical of the hyper-detailed cave art found in diggings in the Fortune Woods, and is often shown to new archaeology students. On a first view, many students claim that it shows humanoid figures with weapons, animals, and a wheel, but SU's Chair of Archaeology, Urtha Bennett, takes great delight in telling them how wrong they are.

What does the cave art actually depict?

(NOTE: It may not be possible to solve the puzzle using the image below.  A higher resolution version is attached to the email copy of this puzzle and is available on request.)

Tuesday, November 2, 2010

032 - Three, Four and Five

Detective Kent Dockland attends at Logidyne Labs to interview Jacki Renquist about the work she's been doing with Hillary Black.

However, he finds Jacki busy in the chemicals storeroom.

"I don't have time for you today, Dockland," Jacki snaps. "I need to measure out four quarts of umbrafan, but one of the idiot new recruits broke my measuring containers. All I have is the barrel of umbrafan, a three quart container, and a five quart container."

"That's a fairly trivial problem, ma'am," said Dockland stoically, and then explained to her how to solve it. "And now maybe you have time for an interview?"

How did Jacki measure out four quarts of umbrafan?

Monday, November 1, 2010

031 - Crackling

Farmer Joe keeps jars full of pre-prepared pork crackling to serve as entrees at Farmer Joe's BBQ Porkatorium.  One jar contains honey-marinated crackling, one jar contains peppered crackling, and one contains a mixture of both.

Unfortunately, Zephyr Cantrell, a regular customer with an odd sense of humour, has switched the labels on Farmer Joe's crackling jars.  According to Zephyr, each of the three jars now bears an incorrect label.  The three labels are "Honey-Marinated", "Peppered" and "Mixed".

Farmer Joe is keen not to waste any of his beloved pork crackling.  Unfortunately, the only way to tell honey-marinated crackling from peppered crackling is to taste it.

From the jar bearing which label should Farmer Joe taste a piece of crackling in order to correctly re-label all three jars?

Sunday, October 31, 2010

030 - Seven Bridges

Serendipity 1's hit TV show Seven Bridges follows the romantic misadventures of a group of attractive singles living in the fictional community of Seven Bridges. The community sprawls across both banks of the Gellis River and also includes two islands in the centre of the river. The riverbanks and islands are connected by a series of bridges, as shown in the attached image.

Famously, the show claims that it is impossible to cross all seven bridges in one voyage without retracing your steps or crossing the same bridge twice, regardless of where you start or finish - a metaphor for life's missed opportunities.

Last year a proposed spin-off, Thirty-Nine Bridges, set on an archipelago of islands, was briefly mooted before being nixed during development.

Is Seven Bridges correct? Is it impossible to cross all seven bridges, as shown in the attached image, without crossing a bridge twice?

And what about the proposed layout of Thirty-Nine Bridges? Is it possible to cross all thirty-nine bridges without crossing a bridge twice?

NOTE: It is not permissible to partly cross bridges - any crossing of a bridge must begin at one end and finish at the opposite end.

Thursday, October 28, 2010

029 - The Devices of Serendipity

Although there are, to date, 53 known Devices, only five are on display in the Serendipity Museum of Local History.

They are stored in a line of five display cases in a high security area of the museum, numbered 1 to 5 from left to right. Each of the five, as is the case with all known Devices, is marked with one of the runic characters of the local ancient language, and each possesses a single unique unexplained property.

1) There are two cases between a Device that emits random ultrasonic noises when exposed to sunlight, and the Device induced by Agnes Tutwillow on its right.

2) The Device that determines the number of iron molecules within 3.8 metres is in the case directly to the left of the Device induced by Yolanda Harkness.

3) There is one case between the Device that anaesthetises its holder, and the Device induced by Jonathan Horacek on its left.

4) The device induced by Brierly Smith is next to The Wheel.

5) The hole punch is not in the fifth case.

6) The Device that makes documents unintelligible is directly to the right of the protractor.

7) The Crossroads is not in the first case.

8) There are two cases between the audio cassette and the protractor.

9) The Crossroads is next to the hole punch.

10) The Knot is next to the pocket calculator.

11) There are two cases between the Device induced by Emilio Argento and The Bear.

12) There is one case between the device induced by Agnes Tutwillow and The Bear on the left.

13) The Wheel is not in the first case.

14) Although one of the Devices boils any liquid it is immersed in, it is not the flashlight.

15) The Thorn is not the pocket calculator.

What does The Knot look like, what does it do, which case is it in, and who induced it?

Wednesday, October 27, 2010

028 - Hagiography

Found left on a street corner:

E * * *

What letters do the three asterisks represent?

Tuesday, October 26, 2010

027 - Heavier Metals

Logidyne Labs is testing a Device. One of the side effects of the Device is to minutely increase the mass of certain alloys in its immediate vicinity.

A scalpel was used in the Device Room today. Per Logidyne procedure, the scalpel will now have to be quarantined until it can be determined to be safe. However, a clumsy assistant has mixed up the scalpel with eight other scalpels.

The nine scalpels are identical in every way, except that the scalpel from the Device room will be heavier than the others.

Using a pair of balancing scales, how can the heavy scalpel be identified in only two weighings?