Word Ladder — Thinking in Shortest Paths
Word Ladder is graph theory in disguise. Here is the hub strategy, when to back up, and how to get your solutions within one or two steps of the optimum.
Word Ladder (#15) gives you two four-letter words and asks you to transform one into the other, changing one letter at a time, with every intermediate word also being a real English word. Lewis Carroll invented this puzzle in 1879 and called it "Doublets". It has a well-defined optimal solution — the shortest path — and the game shows it to you after you solve. This guide is about how to think about that shortest path so that your average solution gets closer to it.
The puzzle is a graph problem
Imagine every four-letter English word as a node in a graph, and connect two nodes with an edge if they differ by exactly one letter. Word Ladder is asking you to find the shortest path between two specified nodes in this graph. There is roughly 4,000 common four-letter English words. The graph is large enough that you cannot enumerate it mentally — but it has structure, and the structure is exploitable.
The key piece of structure: not all letter positions are equal. Some four-letter words have many neighbours (words that differ by one letter); some have few. Words with common letter patterns — words like CARE, CAME, COLD, MAKE — have dozens of neighbours each. Words with unusual letter patterns — words like AZURE-like rarities — have very few. A path through the graph is fastest when it goes through high-neighbour "hub" words.
The hub strategy
When you are given a starting word like FOOT and a target like HEAD, the worst thing you can do is try to change one letter and see what happens. The best thing you can do is identify a hub word that is closer to the target than your start. For FOOT → HEAD, a useful hub is something like HOOT (changing F→H) or FOOT → POOT (no, not a word) → POOR → POUR. The good hubs are common short words: MOOD, MOOR, MOON, MOON, COOL, FOOL, FOUL, FOWL. These have many neighbours and let you pivot the letter pattern toward the target without dead-ending.
A practical approach: write down the start and end words and identify which letters they share. FOOT and HEAD share zero letters in common positions, so the path must change all four positions. Plan which order to change them in. Changing the consonants first (F→H) usually opens more vowel patterns; changing vowels first (O→E) usually opens more consonant patterns. Both work; pick one and commit.
What "shortest" actually means
The shortest solution between two four-letter English words is usually four to six steps. Word Ladder shows you the optimal path length after you solve, and the gap between your solution and the optimum is the score. A typical first attempt: nine or ten steps. A typical fifth attempt: six or seven. After twenty puzzles, most players solve within one or two of the optimum.
The improvement comes from learning the hub words. The same hubs appear over and over because they are dense in the graph. Once you have internalised that MOOR, MOON, MOOD, MOOT are all one letter apart from each other and from many other common words, you stop searching and start routing.
When to back up
Halfway through a long ladder, you sometimes realise your path is going the wrong way — you have changed three letters and the result is now no closer to the target than two steps ago. Back up. The instinct to "make progress no matter what" produces longer ladders than the instinct to "back up and try a different middle". Word Ladder lets you undo, and undoing a step early is much cheaper than completing a wrong path and then having to navigate back. If three consecutive steps have not measurably closed the distance to the target, undo and try a different second step.
Published · 14 May 2026 · Written and signed by Bill