Kominers’s Conundrums: Crack Caesar’s Favorite Code

(Bloomberg Opinion) -- People have used codes and secret messages since time immemorial. They’ve been crucial in wartime, and in some sense underpin all our modern communications security.

They also make great puzzles.

In a cryptogram, you’re given a piece of text that’s been encoded somehow, and have to work out what it says. These can look intimidating at first, but can be extremely satisfying once you unlock them.

Here’s an example:

K’O C ECGUCT EKRJGT!

QJ AGCJ? VJGP YJGTG CTG AQWT NGVVWEG CPF ETQWVQPU?

This cryptogram uses one of simplest and best-known encodings: a letter shift.

We just pick a number between 1 and 25, and replace each letter in the original message by the letter we get if we count that many letters forward in the alphabet (wrapping around if we pass “Z”).

For example, when we shift the letters by 3, we get the substitution “D” for “A”; “E” for “B”; and so forth:

This way of encrypting messages is attributed to Caesar – who apparently used it to send military communications. But it’s not actually that secure. I’ll bet you can figure out the one above without too much trouble.

How do you do that? One trick is to look at very short words, such as “K’O” and that lone “C.” There aren’t many words in English that could fit either pattern – “C,” for example, probably stands in for either “I” or “A.”

And since we know the text was encoded using a letter shift, getting even just one letter correspondence right is enough to decrypt the text. So what happens if we guess that “C” stands for “I” (a shift of 20 letters) or “A” (a shift of just 2)? Give it a try!

Now of course there are other ways to encode messages – and some of them are famously difficult. We’re still working on trying to understand a hieroglyphic cipher first discovered by archaeologists in 1900, as well as a mysterious manuscript from the 15th century. And there’s a cryptic statue at CIA Headquarters that has stumped solvers for decades.

Here’s one that hopefully won’t be quite as impenetrable:

11.4 / .1 3 7.1 2.2 11 16 / 17.4 18.2 9 15 ?

.3 16 / 6.1 12 12.2 11 15 / 16 6.1 16 / 10.1 11 20 / 18.4 14 3 15 / 6.1 17.2 / 16 6.3 15 / 11.4 16.2 18.4 14 16 6 20 / 12 14.4 12.2 14 16 20 !

11.3 2.2 / 7.4 1 / 15.4 9 17.3 11 5

15.2 11 3 / .3 11 / .1 / 4.1 17.4 14.3 16.2 / 15.5 2 6 / 18.4 14 3 / .1 15 / 16 6.2 / " .1 11 15 18.2 14 " / 16.4 / 16 6.3 15 / 12.5 21 21 9.2

Puzzling, right? We might guess that the slashes separate words, but what’s with all those decimal points?

If you figure it out – or even make partial progress – please let me know at skpuzzles@bloomberg.net before midnight Eastern time on Wednesday, May 20. (If you get stuck, there’ll be a hint announced in Bloomberg Opinion Today on Tuesday, May 19. Sign up here.)

And once you’re done with that, you can take a crack at that CIA statue – the artist offered up a new clue in January.

Last Week’s Conundrum

In our Weird Series of Poker, Daffy and Donald played five-card draw with all the cards faceup.  In such a game, you don’t need a poker face, just a solid strategy.

Daffy goes first, but Donald wins if the two hands tie. That means Daffy can’t just grab a royal flush on his first turn – if he were to do so, then Donald could respond by drawing a royal flush of his own.

Instead, what Daffy has to do is block Donald from obtaining a royal flush; one way to do that is to claim the 10 from each suit. Now Donald is on the defensive: if he doesn’t take a high-ranking card from each suit himself, then Daffy can still obtain a royal flush at his discard-and-draw step.

It turns out the best way for Donald to respond is by taking the jack of each suit, since that also stops Daffy from obtaining a straight flush with a jack or higher.

But that leaves Donald with only one more space in his hand. So no matter what Donald does, Daffy can still draw into a 10-high straight flush, and there’s nothing Donald can do to beat that. Thus the basic game is a win for Daffy.

Once we add wild cards to the deck, however, the tables turn: There’s no way Daffy can stop Donald from obtaining a royal flush. Indeed, if Daffy plays a strategy like before where he claims a card from every suit, then he can take at most one wild. So Donald gets the other one and can use it to fill out a royal flush. If instead Daffy claims both wilds on his first turn, then he only gets three other cards – and that means he has to leave at least one suit completely open for Donald.

Iolanthe & Brad Stronger were the first of 118 to call this game; other solvers included Eugenio Arnoux, Matt Hanna, Saang Lee, Winston Luo, David Mirsky, Jenny Mitchell, and Suproteem Sarkar. Ross Rheingans-Yoo solved minutes before his brother Duncan. Varun Krishnan and Amil Merchant characterized a large set of different paths the game can take depending on which cards Daffy picks on his first turn. And The Riddler himself – Zach Wissner-Gross – chimed in with a solution as well; you should check out his puzzle column over at 538 if you haven't already.

The Bonus Round

Popular probability puzzles; Sudoku, but with playing cards; the Ultimate Domino Battle. Call Juneau Alaska’s joke hotline (and/or submit your own joke); read an MI6 Christmas card; or become a Lord or Lady by acquiring a small plot in West Scotland. Beat Super Metroid super quickly – or just watch the animated rendition; then learn how we defeated the Windows “love bug”. And inquiring minds want to know: Can we really restore aging art with math?

In addition to solutions, please send paradoxes, paraphernalia and/or your favorite puzzles to skpuzzles@bloomberg.net.

I first learned the wild-free version of this Conundrum from a fantastic book by Peter Winkler, who attributes it to Martin Gardner. To my knowledge, the version with wild cards is novel.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

Scott Duke Kominers is the MBA Class of 1960 Associate Professor of Business Administration at Harvard Business School, and a faculty affiliate of the Harvard Department of Economics. Previously, he was a junior fellow at the Harvard Society of Fellows and the inaugural research scholar at the Becker Friedman Institute for Research in Economics at the University of Chicago.

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