Here are six new lateral thinking puzzles — play along with us as we try to untangle some perplexing situations using yes-or-no questions.

# Puzzles

# Eban Numbers

What number comes next in this sequence?

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, __

# The Last Digit

A problem from the 1996 Georg Mohr mathematics competition in Denmark:

*n* is a positive integer. The next-to-last digit in the decimal expression of *n*^{2} is 7. What’s the last digit?

# RSS Quiz

Another holiday challenge: The Royal Statistical Society’s 2017 Christmas quiz presents 13 problems that require general knowledge, logic, and lateral thinking but no particular math skills. For example:

4. CAN YOU DIG IT? [11 points]

Identify the following from the clues. What do all ten answers have in common?

- A cockerel of human dimensions, performed by a prolific informer
- William’s book (1956), Charles’s film (1957), or Mike & Al’s song (1971)
- Challenger first appeared here, over a century ago
- A cricketer, a rugby player, or a commentator
- 2001 boy-band album – a remix of “NOW FOR LOUD ROW”
- The official title of Guinness
- One who reigned for almost 999 million seconds
- King’s collection, ordered by cards
- The Bassett country residence, according to Plum
- ATR co-founder, name-checked by “The Tiger” between The Slits and Dickens

You can use any tools or resources you like, including books, search engines, and computer programs. Anyone can enter, and you stand to win £150 if you’re an RSS member. The deadline for entries is January 7. The full quiz is here.

(Thanks, Dave.)

# A Thoughtful Gift

University College London mathematician Matthew Scroggs has created a mathematical Christmas card for *Chalkdust* magazine.

Solve 10 puzzles, convert the answers to base 3, write them in the grid, and color them accordingly to reveal a Christmassy picture.

He’s provided both a PDF and an online version that will color the squares for you.

# Black and White

By Josef Kling. White to mate in two moves.

# Two Puzzles

In 2005 Keele University computer scientist Gordon Rugg published two ciphers to the web.

The first is called the Penitentia Manuscript. The image above is only one panel; you can view and download the whole thing here. Rugg’s website provides one clue: “Most modern codes are based on a shared set of underlying assumptions. He wondered what would happen if you deliberately ignored those assumptions. What sorts of code might that produce?” There’s some more info here.

The second cipher, called the Ricardus Manuscript, was inspired by Rugg’s work on another famous puzzle: “When Gordon was working on the Voynich Manuscript, he started wondering what a real code based on the components of the Voynich Manuscript would look like. This code is the result.” Again, the image below is only a sample; you can find the whole thing here. More info here.

Both of these ciphers have been freely available on the web for more than 10 years, and both remain unsolved. Any takers?

# ‘Tis the Season

Charles Trigg proposed this festive cryptarithm in the *American Mathematical Monthly* in 1956:

MERRY XMAS TO ALL

If each letter is a unique representation of a digit, and each word is a square integer, what are these four numbers?

# The Feynman Ciphers

In 1987, Chris Cole posted a message to the sci.crypt Usenet group:

When I was a graduate student at Caltech, Professor Feynman showed me three samples of code that he had been challenged with by a fellow scientist at Los Alamos and which he had not been able to crack. I also was unable to crack them. I now post them for the net to give it a try.

The first, marked “Easier,” was this:

MEOTAIHSIBRTEWDGLGKNLANEA INOEEPEYSTNPEUOOEHRONLTIR OSDHEOTNPHGAAETOHSZOTTENT KEPADLYPHEODOWCFORRRNLCUE EEEOPGMRLHNNDFTOENEALKEHH EATTHNMESCNSHIRAETDAHLHEM TETRFSWEDOEOENEGFHETAEDGH RLNNGOAAEOCMTURRSLTDIDORE HNHEHNAYVTIERHEENECTRNVIO UOEHOTRNWSAYIFSNSHOEMRTRR EUAUUHOHOOHCDCHTEEISEVRLS KLIHIIAPCHRHSIHPSNWTOIISI SHHNWEMTIEYAFELNRENLEERYI PHBEROTEVPHNTYATIERTIHEEA WTWVHTASETHHSDNGEIEAYNHHH NNHTW

Jack Morrison of NASA’s Jet Propulsion Laboratory had it solved the next day: “It’s a pretty standard transposition: split the text into 5-column pieces, then read from lower right upward.” This yields the opening of Chaucer’s *Canterbury Tales*:

WHANTHATAPRILLEWITHHISSHOURESSOOTET HEDROGHTEOFMARCHHATHPERCEDTOTHEROOT EANDBATHEDEVERYVEYNEINSWICHLICOUROF WHICHVERTUENGENDREDISTHEFLOURWHANZE PHIRUSEEKWITHHISSWEETEBREFTHINSPIRE DHATHINEVERYHOLTANDHEETHTHETENDRECR OPPESANDTHEYONGESONNEHATHINTHERAMHI SHALVECOURSYRONNEANDSMALEFOWELESMAK ENMELODYETHATSLEPENALTHENYGHTWITHOP ENYESOPRIKETHHEMNATUREINHIRCORAGEST HANNELONGENFOLKTOGOONONPILGRIM

But the other two ciphers have never been solved, despite 30 years of trying. Here they are:

#2 (“Harder”)

XUKEXWSLZJUAXUNKIGWFSOZRAWURORKXAOS LHROBXBTKCMUWDVPTFBLMKEFVWMUXTVTWUI DDJVZKBRMCWOIWYDXMLUFPVSHAGSVWUFWOR CWUIDUJCNVTTBERTUNOJUZHVTWKORSVRZSV VFSQXOCMUWPYTRLGBMCYPOJCLRIYTVFCCMU WUFPOXCNMCIWMSKPXEDLYIQKDJWIWCJUMVR CJUMVRKXWURKPSEEIWZVXULEIOETOOFWKBI UXPXUGOWLFPWUSCH

#3 (“New Message”)

WURVFXGJYTHEIZXSQXOBGSVRUDOOJXATBKT ARVIXPYTMYABMVUFXPXKUJVPLSDVTGNGOSI GLWURPKFCVGELLRNNGLPYTFVTPXAJOSCWRO DORWNWSICLFKEMOTGJYCRRAOJVNTODVMNSQ IVICRBICRUDCSKXYPDMDROJUZICRVFWXIFP XIVVIEPYTDOIAVRBOOXWRAKPSZXTZKVROSW CRCFVEESOLWKTOBXAUXVB

Feynman, apparently, couldn’t break them either.

# Decisions

A puzzle by David Silverman:

Able, Baker, and Charlie are playing tag. Able is faster than Baker, who’s faster than Charlie. All three of them start at point P, and Able is “it.” At time -T, Baker runs north and Charlie runs south. After a count that takes time T, Able starts chasing one of the two quarries. The game ends when Able has tagged both Baker and Charlie. If Baker and Charlie maintain their speeds and directions, who should Able chase first to minimize the time required to make the second tag?