The Simple Math Behind Anagrams and Palindromes
What's actually being compared under the hood when a tool checks for an anagram or a palindrome, and why the rule is simpler than it looks.
Published May 3, 2026
Both anagrams and palindromes feel like they require some clever algorithm to detect. In practice, both reduce to a comparison so simple it's almost anticlimactic once you see it written out.
An anagram check is just sorted letters
Two words are anagrams exactly when they contain the same letters, in any order. Sort each word's letters alphabetically, strip spaces and punctuation first, and compare the results: if the sorted letter sequences match exactly, they're anagrams. "Listen" and "silent" both sort down to "eilnst", which is the entire check, nothing more clever than that.
A palindrome check is a reversal comparison
Strip spaces, punctuation, and case, reverse the remaining letters, and compare the reversed version to the original. If they match, it's a palindrome. "A man, a plan, a canal: Panama" only becomes a palindrome once the punctuation and spacing are stripped away, the underlying letters are what's being compared, not the formatted phrase.
Why stripping formatting first matters for both
Neither check is really about the literal string on screen, they're about the underlying sequence of letters. Skipping the normalization step (lowercase, strip non-letters) before comparing would make almost every real-world phrase-level anagram or palindrome fail the check for reasons that have nothing to do with whether it actually is one.