Anagrams

An anagram is a word or phrase formed by rearranging the letters of another, using all the original letters exactly once. Classic examples include listen and silent, or the longer pair astronomer and moon starer, which show how the same set of letters can yield different meanings. Anagrams can involve a single word or a multiword phrase, and in many puzzles spaces and punctuation are ignored during the rearrangement.

The word 'anagram' comes from Greek ana- 'again' and grámma 'letter'. Anagrams have appeared in many cultures and historical periods, and they are widely used in word games, literary puzzles, and cryptographic exercises. They are valuable for studies of language play, phonology, and the distribution of letters within a text.

Most analyses assume a 'perfect' anagram, where the transformed form uses exactly the same letters with identical counts. When solving or constructing anagrams, it is common to ignore case and punctuation, and to treat spaces as irrelevant. Variants include phrasal anagrams and semantically playful forms. Antigrams are a related idea in which the rearrangement yields words with opposite or contrasting meanings.

In computation, determining whether two strings are anagrams is a standard problem. Techniques include sorting the letters or counting character frequencies, often with linear time complexity relative to the string length. Practical tools use canonical representations, such as a sorted sequence or a multiset of counts, to enable fast lookups in dictionaries of known anagrams or to power word-game solvers.