Anagrams, Palindromes, Cryptarithms and Alphametics

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Author, Physician, Philosopher, Polyhistor

3 years ago

In community: The Power of Words(4be2)

Topics: Words, Word Games, Numbers

In "La Dame de Montsoreau", Alexandre Dumas père lets Chicot, the court jester of Henri III, make an anagram of Henri's name. He got "Vilain Herodes" by "Henri de Valois". Only a court jester could show such a lack of respect to a king in those days! As we can see, the one is obtained from the other by rearranging the letters. That is to say, one is an anagram of the other.

In Cabbalism, letters are seen as magical, somehow related to the very essence of reality. Words and phrases that can be formed by the same set of letters are related, on a profound metaphysical level they share something... By that follows that an anagram of someone's name would reveal something about that person's character or destiny.

Anagrams can be used for fun too, and have been so since Antiquity. Some sources give Lycophron (Greek poet, 285-247 BC) the honour of having invented the concept, but I seriously doubt that. The Greeks rarely invented anything themselves, but gathered their knowledge from older high(er) cultures like Egypt, Babylonia, and India. It would be strange if anagrams were not known in old India, although - of course - applied with syllabic script.

Various anagrams on Shakespeare's texts are famous, since they are used to "prove" that someone else wrote his plays. In "Love's Labour's Lost" there is a long word "honorificabilitudinitatibus" (I hope I got all these letters right!). An anagram of that is the Latin sentence: "Hi ludi F. Baconis nati tuiti orbi", which means "These plays, F.Bacon's offspring, are preserved for the world." It is possible to make other anagrams from Shakespeare's texts, or use other cryptographic systems, "proving" that they were written by many others too. [See William F. & Elizabeth S. Friedman, "The Shakespearian Ciphers Examined," Cambridge 1957.]

Sometimes anagrams are used to form pseudonyms too, but their main use is as a play with words. A man named Mike Keith is said to have made an anagram of the entire text of the novel Moby Dick. I can see little reason to spend time and energy on such constructs. It is too long even to be fun.

A palindrome is a word or sentence that reads the same from left to right and from right to left; that is, if the order of the letters is reversed, the original appears again. Like in"Anna" or the oldest recorded palindrome in English: "Lewd I did live, & evil did I dwel."

The Old Greeks had palindromes like this: Nipson anomemata me monan opsin, [in Greek "ps" is one letter] = wash the sin as well as the face.

Sotades, a Greek poet, used them frequently. They even came to be called "sotadics".

Always imitating the Greeks, the Romans used them; as in this riddle:

In girum imus nocte et consumimur igni = we enter the circle after dark and are consumed by fire. It can be about the cycle of the months, or about an insect.

The earliest known two-dimensional palindrome was found in the Roman city Herculaneum. There is no reason, however, to believe that it was the first one ever.

S A T O R

A R E P O

T E N E T

O P E R A

R O T A S

SATOR AREPO TENET OPERA ROTAS = the sower Arepo leads the plough (or the wheel). Other interpretations might be possible.

There is a whole literature about the sator square and its meaning. Magic qualities have been attributed to it, and it has been thought to protect against the devil.

Palindromes are well known in India, and examples can be found in both Tamil and Sanskrit, although the syllabic writing makes the technique a bit different.

In Chinese, a palindrome is a sequence of signs that can be reversed.

So far this article has been dealing with concepts having to do with words. Cryptarithms and alphametics are number puzzles, not genuine word games, but I include them here because they are related to the material, and because an alphametic at least looks like a word game.

In a cryptarithm, the digits of an arithmetical calculation are replaced with letters (or other symbols). To solve it one has to identify a digit for each letter. If the letters form genuine words, the cryptarithm is called an alphametic.

Solving an alphametic require no special mathematical knowledge, just addition, subtraction, multiplication and division - and some logic. Two letters can never stand for the same digit, and no alphametic can begin with zero.

To illustrate this, let us together solve this one:

(BE)(BE) = MOB

1. If B=4, we would get a four-digit result. But MOB contains just three digits, so B<4 (< means "less than"). Since it cannot be zero, it has to be 1, 2, or 3.

2. Now we look at E. (E)(E) [E times E] must end in B. If we try all possible values of E, we find that only two gives a result [(E)(E)] that ends in 1, 2, or 3; namely E=1 and E=9. But E=1 would give B=1 too, and two letters could not stand for the same digit, so E=9; and consequently B=1.

3. Then we have (BE)(BE)=(19)(19)=361=MOB. So we get B=1, E=9, M=3, O=6.

Some alphametics are doubly true. Can you solve this?

ONE

TWO

+ FIVE

======

EIGHT

Or try these:

(BE)(BE)=ARE

(BE)(BE)=ABE

(BE)(BE)=SAD (this one has four solutions)

If you are amused by this sort of puzzles, why not try to solve them before looking further? But here are the answers: