Games & Puzzles
Word Ladder - Transform Words One Letter at a Time
Transform one word into another by changing one letter at a time, with each step being a valid word.
Hint: Change one letter at a time.
About Word Ladder
Word Ladder (originally called "Doublets") is a word puzzle invented by Lewis Carroll in 1877. The goal is to transform one word into another by changing only one letter at a time, with each intermediate step also being a valid word.
Example
CAT -> DOG: cat -> bat -> bad -> bag -> ban -> tan -> ton -> too -> too -> dog (one possible solution).
Strategy
- Work from both ends: find a word that is one letter away from the start word AND one letter away from the target word. Meeting in the middle reduces the total steps needed.
- Change consonants, not vowels first: consonant changes often preserve word patterns and create more valid intermediate words.
- Think about bridges: some short words (HIT, SIT, SAT, SAP, CAP, CAT) connect many common four-letter families.
Historical note
Lewis Carroll published Doublets puzzles weekly in Vanity Fair from 1879 to 1881 and compiled them in a book in 1879. He considered them an exercise in “precision of thought.” Word Ladders later became a classic computer science problem: finding the shortest word ladder between two words can be solved with a breadth-first search across a graph of valid words, where each word is a node and edges connect words that differ by exactly one letter.
Graph theory connection
A word ladder puzzle is precisely a shortest-path problem on a graph:
- Nodes: each valid word in the dictionary.
- Edges: two words are connected if they differ by exactly one letter.
- Solution: a BFS (breadth-first search) from the start word finds the shortest path to the target word.
This is a classic CS teaching example used to introduce graph representations, adjacency lists, and BFS in algorithms courses.
Impossible ladders
Not all word pairs can be connected. The word graph is not fully connected - some words form isolated clusters or are unreachable from others (e.g., words with unusual letter patterns). To detect whether a ladder exists, BFS terminates either when the target is found or when the queue is exhausted without finding it.
Famous word ladders from Lewis Carroll
Carroll’s original puzzles, called Doublets, appeared in Vanity Fair (1879–1881). One of his most famous chains:
HEAD -> heal -> teal -> tell -> tall -> TAIL (5 steps)Carroll challenged readers to find the shortest chain, which is equivalent to asking for the BFS shortest path in the word graph.