An **anagram** (from the Greek *ana* = “to return” or “to repeat” + *graphein* = “to write”) is a kind of word , resulting from the rearrangement of the letters of a word or expression to produce other words or expressions,Anagrams are often expressed in the form of an equation, with symbols of equality (=) separating the original objective and the resulting anagram. ** Actor = Rota** is an example of a simple anagram expressed in this way. In a more advanced, sophisticated form of anagram, the objective is to “discover” a result that has a linguistic meaning that defines or comments on the original objective in a humorous or ironic way. When the objective and the resulting anagram form a complete sentence, a tilde (~) is commonly used, rather than an equal sign; for example:

*Semolina ~ Is no meal*.

## Index

- 1Examples of constrained writing
- 2Mathematics
- 3Combinatorial Analysis
- 1Anagrams with repeated letters

- 4Ferdinand de Saussure
- 5Notes and references
- 6External links

**Examples of constrained writing **

**Anagram**: Word or expression made using exactly the same letters as the original word or expression. Examples: The question, in Latin , ”*Quid est veritas?*” (*What is the truth?*), And the answer ”*Est vir qui adest*” (*It is the man in front of you*)**Pangrama**: Pangrama is a phrase that uses all the letters of the alphabet. Examples: “*A small xereta tortoise saw ten happy storks.*“; “*Blitz arrests Wykie, squinting with a fake check.*“; “*Gazeta today publishes in the newspaper a brief cleaning note in the feast.*“; “*The quick brown fox jumps over the lazy dog.*“**Anigram**: Anagram that animates itself by shuffling the letters in a computer animation, which commonly occurs in GIFs or animations developed in Flash .^{[ 1 ]}**Anugrama**: Phrase in which your anagram has the same meaning as the original phrase. Examples: ”*Eleven plus two ~ Twelve plus one*“; “To*pass without knowing: we always have time, if we start reading ~ Start over, but be in a hurry. Remember: we cannot do without time*“.

**Anagram In Mathematics **

To find an anagram mathematically, just use the formula ((ab) / c) +1, where:

- A = number of anagram;
- B = last character or the difference of dividing B by C (B \ C in basic, or mod of the windows calculator);
- C = number of characters.

**Combinatorial Analysis**

To obtain the number of possible anagrams from the letters of a certain word, as long as they do not have repeated letters, just perform the permutation ({\ displaystyle P}) with the total number of letters, examples:

- Be {\ displaystyle n}the number of letters of a given word and {\ displaystyle Na} the number of anagrams we have:

{\ displaystyle Na = P (n) -1 = n! -1}

One must subtract one of the combinations from the equation, because a word cannot be an anagram of it! Example: the word ** love** is an anagram of

**, but**

*rome***is not an anagram of**

*rome***. So there is the{\ displaystyle -1} in the equation.**

*rome*Note that, by this method, many letter combinations will not form words.

- How many anagrams are obtained from the word DANIEL?

DANIEL has 6 letters, therefore, {\ displaystyle n = 6};

{\ displaystyle {\ begin {aligned} Na & \ = \ P (6) -1 \\ & \ = \ 6! -1 \\ & \ = \ 6 \ times 5 \ times 4 \ times 3 \ times 2 \ times 1-1 \\ & \ = \ 719 {\ text {anagrams}} \ end {aligned}}}

### Anagrams with repeated letters

If we have repeated letters in the word, we must divide the result by {\ displaystyle P (n)} through the permutations of each repeated letter, according to the formula.{\ displaystyle \ mathbb {P} _ {n} ^ {r = \ {{r_ {1}, r_ {2}, r_ {3}, …, r_ {n} \}}} = {\ frac {n!} {r_ {1}! \ cdot r_ {2}! \ cdot r_ {3}! \ cdot {\ text {…}} \ times r_ {n}!}}}

**Examples**

- How many anagrams are obtained from the word PARALELEPIPEDO?

Total letters {\ displaystyle n = 14};

Number of repetitions: {\ displaystyle r = \ {p = 3; a = 2; l = 2; e = 3 \}}

Therefore:

{\ displaystyle {\ begin {aligned} Na & \ = \ {P} _ {14} ^ {3,2,2,3} \\ Na & \ = \ {\ frac {14!} {3! \ cdot 2! \ cdot 2! \ cdot 3!}} \\ Na & \ = \ {\ frac {14529715200 \ cdot 3!} {3! \ cdot 24}} \\ Na & \ = \ {\ frac {14529715200} {24}} \\ Na & \ = \ 605.404.800 \ end {aligned}}}

- If all the anagrams of the word SUDAM are listed in alphabetical order and numbered with whole numbers starting from the 1st, will the word MADUS correspond to the anagram of number?

In the problem it is necessary to count the anagrams in alphabetical order; therefore, for each position of the letters in the word there will be so many anagrams that are missing to complete the number{\ displaystyle n} of letters of the word;

The list of alphabetically ordered letters is: {\ displaystyle \ {A, D, M, S, U \}}, with {\ displaystyle n = 6};

{\ displaystyle \ sum {A (4!), D (4!), MAD (2!)} = 50}

**Ferdinand de Saussure**

Ferdinand de Saussure, father of modern Linguistics, studied, long before giving his *Cours de Linguistique Générale* (General Linguistics Course, ed. Cultrix), the anagrammatic phenomenon in Greek-Latin prose and poetry. According to his study, by an incomplete sign, it was common practice for the poets of Antiquity to construct the verses on top of certain anagrams, basing such metrifications on pre-established rules on equivalent quantities of consonants and vowels and the arrangement of the letters forming the anagram in the verses. ^{[ 2 ]}