Anagram vs Palindrome

Two different questions

A palindrome is about order. LEVEL, RADAR, CIVIC and KAYAK read identically from either end, and the test is simply to reverse the word and compare. Nothing is rearranged; the word is read twice.

An anagram is about content. It asks whether two words hold the same letters in the same numbers, whatever their order. LISTEN → SILENT is an anagram, and neither word is a palindrome. KAYAK is a palindrome, and no other English word uses its letters. Knowing one property tells you nothing about the other.

Where they overlap

Some words are both. REFER is a palindrome, and REFER → FREER is an anagram, so one word has both properties at once. It is rare, because a palindrome's letters are arranged so symmetrically that there is seldom another word hiding in them.

Reversals sit neatly between the two ideas. STRESSED → DESSERTS, DRAWER → REWARD and LIVED → DEVIL are words that spell a different word backwards. Every reversal is an anagram, because it uses exactly the same letters. None of them is a palindrome, because the backwards reading is a different word. Word lovers call these semordnilaps, which is "palindromes" spelled backwards.

The third test: could it become a palindrome?

There is a question that joins the two ideas: can these letters be rearranged into something that reads the same both ways? The answer depends only on counting. In a palindrome, letters pair up around the centre, so at most one letter can appear an odd number of times. That single odd letter sits in the middle.

LOTTO has two Os, two Ts and one L, so its letters could form the palindrome TOLOT, even though that is not a word. LISTEN has six different letters, each appearing once. That is six odd counts, so no rearrangement of LISTEN can ever read the same backwards.

The checker at the top of this page runs all three tests on one word at once, and they regularly disagree. Watching them disagree is the fastest way to see that these are three different questions, not three versions of one.

Why people mix them up

Both are games played with the letters of a single word, both turn up in the same puzzle books, and both have Greek names that sound technical. The confusion is strongest with reversals, because a word read backwards feels like a palindrome even when it is really an anagram. A simple way to keep them apart: a palindrome asks "is it the same backwards?", and an anagram asks "is it made of the same letters?". Only the second question lets you move letters around.

Phrases and numbers

Both ideas stretch to phrases. "A man, a plan, a canal: Panama" is a palindrome once spaces and punctuation are ignored, which is the same convention anagrams use. Palindromes also exist outside words: 12321 is a palindromic number, and some dates read the same in both directions.