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Competition: Cryptogram Puzzle

Author and mathematician Josh Holden has come up with a nice puzzle — so we’re posting it as a competition. If you think you can decrypt the message below, send in the decrypted message and a one- or two-sentence description of the mathematical principle behind the encryption key to root@aperiodical.com.  The first correct entry received will win a copy of Josh’s book, The Mathematics of Secrets.

The technical name for the “cryptograms” found in many newspapers and magazines is monoalphabetic monographic substitution ciphers — monographic meaning that they make substitutions one letter at a time and monoalphabetic meaning that the substitution rule is the same every time a given letter appears in the message.

Most often the easiest way to start solving these is to look at one-letter words which are usually “I” or “a”, then two-letter words, etc. If the breaks between the words are removed, then you might use the fact that in a typical English text the letter “e” will occur about 13% of the time, followed by “t” and “a” at 7-8% and others farther behind.

What then should we make of the following cryptogram?

YOFQX RGLQT GCQPB FFGQJ IQOFT SYVQH FSFQV FTYFC QJGQY OFRSQ YOSJG FQHOF GQYOF NQTSS REFCQ HRYOQ TQLSF TYQZS JHCQT VVFDW AFCQT WJBYQ YOFDQ TAAQV JSYVQ JIQAR YYAFQ WRSCV QTGCQ WFTVY VQTVQ HFAAQ TVQYO FQHOJ AFQMT ZXQJI QZTSC VQYOF QXGTE FQHTV QVYTG CRGLQ WFIJS FQYOF DQRGQ ZOTRG VQHRY OQTQV JACRF SQJGQ FTZOQ VRCFQ YJQLB TSCQO RDQTG CQGFT SQYOF QXRGL QHTVQ YOFQH ORYFQ STWWR YQHRY OQTQY SBDMF YQRGQ JGFQO TGCQT GCQTQ VZSJA AQJIQ MTSZO DFGYQ RGQYO FQJYO FS

The letter “Q” appears almost 20% of the time, followed by “F” at about 10%, and “Y” and “T” at about 8%. The original text is English (in fact it’s from a famous work of children’s literature) and it doesn’t have a particularly odd distribution of letters. Can you decrypt the message? For bonus points, can you figure out what is mathematically interesting about the encryption key?

Katie’s Binary Nails Tutorial – and a puzzle

I’ve just posted my latest YouTube video, in which I explain how to use binary numbers to jazz up your nail varnish:

Alongside this video, I also have an associated puzzle for you to think about.

Review: Pythagoria

pythagoria

Pythagoria is a puzzle game for PCs. It’s the same idea as Naoki Inaba’s Area Maze: you’re shown a geometric construction, not drawn to scale, and you have to work out a missing length or an area.

Each puzzle is constructed so that it can be solved without ever dealing with fractions, though what exactly that means is up for debate. Whatever it means, it keeps you from breaking out pen and paper to solve a problem algebraically, when you know there should be a way of doing it in your head.

Take the 30 second arithmetic challenge

My wife’s grandmother is a fearsome character. She’s in her nineties but still has all her wits about her. In fact, she’s got more than her fair share of wits. Whenever we visit her, she hits me with a barrage of questions and puzzles collected from the last several decades of TV quiz shows and newspaper games pages. My worth as a grandson-in-law is directly proportional to how many answers I get right.

One of her favourite modes of attack is the “30 Second Challenge” from the Daily Mail. It looks like this:

quiz0512_800x310

You start with the number on the left, then follow the instructions reading right until you get to the answer at the end. It’s one of Grandma’s favourites because it’s very hard to do in your head when she’s just reading it out!

I decided it would be a fun Sunday morning mental excursion to make a random 30 second challenge generator

#thatlogicproblem round-up

C: $K_A m; \\ K_B d.$

A: $\neg K_A d; \\ m \vDash \neg K_B m.$

B: $d \not\vDash K_B m; \\ (K_A(\neg K_B m)) \vDash K_B (m,d).$

A: $m \wedge K_B(m,d) \vDash K_A (m,d).$

Albert, Bernard and Cheryl have had a busy week. They’re the stars of #thatlogicproblem, a question from a Singapore maths test that was posted to Facebook by a TV presenter and quickly sent the internet deduction-crazy.

First of all: no, it’s not meant to be answered by an average Singaporean student. It’s a hard question from a schools Olympiad test.

From the Mailbag: Golfing Combinatorics

Sam’s dad is in a mathematical conundrum – so she’s asked Katie, one of our editors, if maths can save the day.

From the Sartorial Arts Journal, New York, 1901Dear The Aperiodical,

My dad is going away on a golfing holiday with seven of his friends and, since I know a little bit about mathematics, he’s asked me to help him work out the best way to arrange the teams for the week. I’ve tried to work out a solution, but can’t seem to find one that fits.

They’ll be playing 5 games during the week, on 5 different days, and they’d like to split the group of 8 people into two teams of four each day. The problem is, they’d each like to play with each of their friends roughly the same amount – so each golfer should be on the same team as each other golfer at least twice, but no more than three times.

Can you help me figure it out?

Sam Coates, Manchester

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