Fiendish cryptic puzzle

The latest offering from Harper's.  Took me way too long. 

Very challenging cryptic puzzle

This was the cryptic in this month's issue of Harper's.  Each of the numbered clues contains two cryptic clues, with no indication of where one ends and the other starts, and with no guidance as to whether the answer goes on the right or left side of the grid.

For puzzle enthusiasts - updated with answers

Each year the Royal Statistical Society posts a "Christmas Quiz."  The 2017 Christmas Quiz is here.

The embed above is a convenient image, but is not representative of the quiz as a whole, much of which is not "mathematical."

I've got questions 1b and 12 mostly done, and may work on some more as time permits, but I'm saving most of my energy for the pending release of the King William's College General Knowledge Quiz, which should be out any day now.  Great fun and an immense challenge.

Related: Here's a good puzzle for you (with links to the 2016 RSS quiz - and answers).

Addendum:  Answers to the 2017 RSS Christmas Quiz now in the Comments.

Word lengths in crossword puzzles

I found this interesting because I keep an ongoing record of how long it takes me to solve the daily crossword puzzle (I use the free one in the Los Angeles Times).

Although the graph is entitled "Average word length for NYTimes Crossword answers, 1994-2017," it should more properly be described as "entry length," since quite a few of the answers on the late-in-the-week puzzles are multiple-word entries.

I found this graph at the Data Is Beautiful subreddit, where the discussion thread has some interesting observations about the software puzzlemakers use in their craft.

FWIW, my worst time on a Thursday puzzle this past year occurred in one this past December which required entering the following "words" -

sentildeor
becircumflexte
soupccedillaon
uumlautber

- which came from the following clues:

Terragona title, in detail?
Arles animal, in detail?
Toulouse trace, in detail?
Augsburg above, in detail?

Fiendish.

Hexagon geometry puzzle

This one you can do in your head.  That's what I did.  Got it wrong, but I was really, really, close...

For the answer, go to Brilliant or to Data Genetics.

This is a cryptogram math puzzle

Designed for the math aficianado, not the wordsmith.

Each of the 9 letters in the equation represents a different one-digit number from 1-9 (the denominators are double-digit numbers, not multiplied numbers). 

There is a unique solution.  You can view it at DataGenetics.

"Cat-behind-the-door" puzzle

From The Guardian's Mathematics column today:

A straight corridor has 7 doors along one side. Behind one of the doors sits a cat. Your mission is to find the cat by opening the correct door. Each day you can open only one door. If the cat is there, you win. You are officially smarter than a cat. If the cat is not there, the door closes, and you must wait until the next day before you can open a door again.

If the cat was always to sit behind the same door, you would be able to find it in at most seven days, by opening each door in turn. But this mischievous moggy is restless. Every night it moves one door either to the left or to the right. 

How many days do you now need to make sure you can catch the cat? 

Clarifications at the link.  The answer will be posted at The Guardian later today.  Some reader here may be able to solve this.

Cat photo for those who don't like maths:

Chess problem

From The Telegraph:

The puzzle above may seem hopeless for white, with just a King and four pawns remaining, but it is possible to draw and even win.

Scientists have constructed it in a way to confound a chess computer, which would normally consider that it is a win for black.  However an average chess-playing human should be able to see that a draw is possible.  A chess computer struggles because it looks like an impossible position, even though it is perfectly legal...

The first person who can demonstrate the solution legally will receive a bonus prize.

Both humans, computers and even quantum computers are invited to play the game and solutions should be emailed to puzzles@penroseinstitute.com.

For those who like to take quizzes...

A challenging one for New Year's Eve.  Answers at The Guardian.

RSS Christmas Quiz, question 10

I'm revisiting the 2016 Christmas Quiz for the Royal Statistical Society, seeking help to the answers for the above question.  I think I have 9 of them, but I give up on the others and would like your input.  (The official answers will be published by the RSS in mid-January).  (Addendum January 2017:  The answers to all the quiz questions are now posted.)

In case you want to try your hand at them first, I'll place my answers below the fold (click on "read more" when you want to see them:

Here's a good puzzle for you

 

12. A Matter of Belief

Fold up the string of letters below so it fits in the grid. Squares of the same colour (except white) must not contain contiguous letters in the string.

H E R U I H I E I N B U L L L D S F N D E I I S B

Who is the indicated person (of particular interest to members of the Royal Statistical Society)?

(4 points for the completed grid: 1 point for identifying the indicated person)

This question is one of thirteen components of the Royal Statistical Society Christmas Quiz for 2016.  Some of them appear to be fiendishly difficult.  This one is solvable with simple logic.  I'll place a clue to the answer in the Comments for this post.

(Please don't post answers to any of the other quiz questions in the comments; I'm still working on them.  Tx.)

Addendum January 2017:  The answers to all the quiz questions are now posted.

So you think you're pretty smart...

Try answering these questions from the Royal Statistical Society's Christmas Quiz for 2015:

1. Begin (5 points)
What might, in turn, be represented by a Buckeye, a Boxer, a Berkshire, a Brown, a Brahman, a Bengal, a Beveren, a Bearded, a Boa, a Brumby, a Boreray and (in 2016) a Barbary?

5. Out of Place (4 points)
(a) Explain why, compared with ‘sweet milk’, ‘little cut off’, ‘recooked’, ‘beautiful country’ and ‘tired’, ‘slice’ is out of place.
(b) Similarly, which one of ‘iron’, ‘little blackbird’, ‘black pine’, ‘musky’, ‘tears of Christ’ and ‘white savage’ is out of place?

7. www.capitals.table (6 points)
If Brussels=4, Santiago=17, Buenos Aires=18, Ottawa=20 and Brasilia=35, what is Canberra?

9. In the sky, on the lea (8 points)
What might have inspired whom to write the following, and where has a line been omitted?
“Nature, in tooth and claw,
In lands of palm, of blossom
That sparkled on the field
And on a simple village,
And drowned in yonder living
By hooded doctors.”

10. Diagram (6 points)
Explain the diagram, and give appropriate row and column labels.

Solutions (and more questions) at the link.

I'm eagerly awaiting the 2016 King William's College General Knowledge Paper for 2016-17.  It should be published in The Guardian this coming week. (Here's last year's quiz.) (And the answers.)

"Ants on a stick" math puzzle

Four red ants and two black ants are walking along the edge of a one metre stick. The four red ants, called Alf, Bert, Derek and Ethel, are all walking from left to right as we look at the diagram, and the two black ants, Charlie and Freda, are walking from right to left.

The ants always walk at exactly one centimetre per second. Whenever they bump into another ant, they immediately turn around and walk in the other direction. And whenever they get to the end of a stick, they fall off.

Alf starts at the left hand end of the stick, while Bert starts 20.2 cm from the left, Derek is at 38.7cm, Ethel is at 64.9cm and Freda is at 81.8cm.

Charlie’s position is not known - all we know is that he starts somewhere between Bert and Derek.

So here is the puzzle: Which ant is the last to fall off the stick? And how long will it be before he or she does fall off?

It's not actually that difficult.  You can solve it in your head if you start with the right conceptual framework (true of so many math puzzles).  For the purposes of the puzzle, the length of an ant is assumed to be zero.

The answer is at The Guardian.

Crouching snowmen, hidden panda

I gave up trying to locate the panda hidden among these snowmen.  The answer is shown at The Telegraph.

NDXOXCHWDRGHDXORVI

Can you decipher these letters?

A medieval sword that carries a mysterious inscription has baffled historians for centuries. Little is known about [the] double-edged weapon, least of all the meaning behind a cryptic 18-letter message running down the central groove which reads: NDXOXCHWDRGHDXORVI.

Now The British Library have appealed for the public’s help in cracking the conundrum...

The weapon was found at the bottom of the River Witham in Lincolnshire in 1825, but it’s believed the 13th century sword originally belonged to a medieval knight...

The indecipherable inscription is inlaid with gold wire and experts have speculated the letters are a religious invocation since the language is unknown...

Anne Robertson reckons the letters may be the first from each line of a poem – something that’s been seen on other medieval artefacts. A number of people have picked out certain letters which had particular meanings in Latin at the time, such as ND standing for ‘nostrum dominus’ meaning our Lord, and ‘X’ for Christ. Harrison thinks this is the most probable idea so far 'but then it gets more complicated'. 'It's been suggested in the past that it's a relgious inscription and the sword may have been dropped in the river on purpose [for religious reasons] which was not uncommon...'

More details, pix and a video at the link.  I should probably carve TYWKIWDBI on something...

A 12th-century rebus

It reads “Well fare, mi lady Cateryne”.  Details explained* in a post at Erik Kwakkel's always-interesting blog.

* the explication there says that "cater" was the term used for a die - but I think "cater" refers just to the 4-spot on a die ("the terms ace, deuce, trey, cater, cinque and sice have been made obsolete by one to six...")  Anyone know for sure?  Never mind - I found it:

The full set of numbers for the six sides of a die are ace, deuce, trey, cater, cinque, sice. They are from Old French (cf un, deux, trois, quatre, cinq, six of modern French). Ace is originally from the Latin for 'unit'.

Math puzzle

Three spaceships land randomly on a spherical planet.

What is the probability that all three will land in the same hemisphere?

Answer below the fold.

Deriving "the number of the Beast" from 123456789

I found this in a Martin Gardner column in a back issue of Isaac Asimov's Science Fiction Magazine.

The "number of the Beast" (666) can be derived in eight different ways by placing + and - signs in the sequence 123456789.  Only plus and minus signs may be used, and the numbers have to stay in that order.

To me, the most remarkable solution is this one:

+123 +456 +78 +9 

There are five solutions that include the number 678, such as:

-1 +2 -3 +4 -5 +678 -9

And two solutions that use 567 as a component.

I'll defer posting those, to allow those of you who enjoy math puzzles to post your discoveries in the comments.  (btw, there are also five solutions using the descending order 987654321).

Update: Rob from Amersfoort has posted the other answers in the comments.

This photograph is a cryptogram

I found this fascinating photo (click for bigger) and story at Cabinet.  Some brief excerpts:

At first glance, the photo looks like a standard-issue keepsake of the kind owned by anyone who has served in the military. Yet Friedman found it so significant that he had a second, larger copy framed for the wall of his study. When he looked at the oblong image, taken in Aurora, Illinois, on a winter’s day in 1918, what did Friedman see? He saw seventy-one officers, soon to be sent to the war in France, for whom he had designed a crash course on the theory and practice of cryptology...

And he saw a coded message, hiding in plain sight. As a note on the back of the larger print explains, the image is a cryptogram in which people stand in for letters; and thanks to Friedman’s careful positioning, they spell out the words “KNOWLEDGE IS POWER.” (Or rather they almost do: for one thing, they were four people short of the number needed to complete the “R.”)

Several readers here will recognize the phrase as a signature quote by Sir Francis Bacon, who was famous for his work with cryptography, and one reader (Dan Noland) can decipher the code without hints.  For the rest of us, a brief explanation that the code is a "biliteral" cipher -

The cipher was based, as the name “biliteral” suggests, on a system using only two letters—or, more precisely, one where each letter in the alphabet is represented by some combination of a’s and b’s... Bacon realized that it was possible to represent all twenty-six letters in permutations of only two by using groups of five...

Details of the coding are presented at the Cabinet link, where this important point is offered:

But Bacon added a further twist to the ancient art of steganography, the general name for the practice of concealing messages through the use of disguise and deception. In the biliteral cipher, the cover-text need not, in fact, be “text” at all: the a’s and b’s can be represented by two types of anything—pluses and minuses, flowers of different kinds or colors, even (literally) apples and oranges—and this, for Bacon, is what gives his biliteral system the greatest power of all. 

Here's an example of an image with an embedded biliteral cipher:

and in a page of sheet music (hidden message “Enemy advancing right / We march at daybreak”):

This is a fascinating subject, and one which scales up impressively in the modern digital world.  The image below, for example, contains the complete text of Herman Melville's novels Moby-Dick and Typee (319,000 words):

Details about this steganograph at the flickr page of krazydad/jbum.  And there's much more at the Cabinet article.

How to survive if you're placed in a blender

The Wall Street Journal provided several answers to that dilemna in an article entitled "How to Ace a Google Interview."

You are shrunk to the height of a nickel and thrown into a blender. Your mass is reduced so that your density is the same as usual. The blades start moving in 60 seconds. What do you do?

These questions, posted by job candidates on Glassdoor.com, aren't from some wacky Silicon Valley start-up—they're asked of applicants at AT&T, Johnson & Johnson and Bank of America, respectively.

Goldman Sachs interviewers ask candidates the firm's stock price. Morgan Stanley asks interviewees to name a recent story they've read in the Financial Times—apparently, a lot can't. J.P. Morgan Chase asks the value of pi. (It's thought to be instructive to see how many digits the candidate can recite.)

Here are two additional, more standard math-type interview questions reportedly used at Google interviews -

3. Using only a four-minute hourglass and a seven-minute hourglass, measure exactly nine minutes—without the process taking longer than nine minutes.  
 
4. A book has N pages, numbered the usual way, from 1 to N. The total number of digits in the page numbers is 1,095. How many pages does the book have?

Answers to these and the blender question at the link.

Addendum: A hat tip to an anonymous reader who found an article written by someone with personal experience on a Google hiring committee.  The story that Google uses lateral thinking questions in their interview process is an urban legend (though other companies may do so).  Details at the link.