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How the puzzles are made
A word graph, a breadth-first search, and a rule that keeps par achievable.
Building the word graph
Rung a Day uses about 2,300 common four-letter English words. Each word becomes a point in a graph, and two points are joined when the words differ by exactly one letter in the same position. A ladder is a path through that graph, and you can picture it as a map where every short road is a single letter change. Because four-letter words are more tightly connected than five-letter ones, the graph is dense, which is why four-letter ladders are usually easier and shorter. A word with many neighbours offers many possible next steps, while a word with one neighbour leaves you a single direction. Obscure words, dialect words and proper nouns stay out, so every step you take is a word you could reasonably use.
Finding the shortest route
Once the graph exists, we search it exhaustively. A breadth-first search starts at the first word, visits each neighbour, then each neighbour of those neighbours, and stops as soon as it reaches the second word. The number of steps in that ladder is par. Because the search has already checked every shorter route, par is the true minimum for our word list rather than an estimate. That matters when you play. If the page says par is five, no four-step ladder exists in the graph, so you never chase a target we guessed at. Building a ladder by hand can feel longer, because you work forwards from one word while the search works outwards from the start.
Restricting both ends
A shortest path is only useful if both ends are words you recognise. Short routes between two obscure words are easy to find and no fun to solve, so the endpoints come from the common list just as every intermediate step does. If a candidate puzzle needs a word most people would have to look up, we drop it and search again. The same rule protects the middle of the ladder. You will sometimes spot a tempting ladder outside the list, and it may even be shorter than par. A route that leans on a dialect spelling or a name may exist in a larger dictionary, but it will not appear here.
Setting the difficulty curve
Par gives us a number to sort by. A short ladder may ask you to spot one useful swap, while a long one asks you to hold several partial routes in mind at once. We use that range when ordering puzzles, so the week moves between easier and harder ladders instead of stacking the longest ones together. Because par is measured rather than guessed, two days can be compared honestly. Up to three hints are available if a puzzle refuses to move, and a hint reveals one letter of a shortest route rather than a whole answer. The aim is a curve you can follow day by day, where a hard ladder still feels fair.
Questions
Why is par not just an estimate?
Every puzzle is searched exhaustively between its two words before publication, so par is the length of the shortest route in our list. A shorter ladder may exist in a larger dictionary, but not in the graph used for play.
Can a ladder use a word I have never seen?
No. Every rung comes from the same list of common four-letter words, and obscure words, dialect words and proper nouns are rejected. If a step looks unusual, check the spelling, because the word is one the list accepts.
How many hints can I use?
You can take up to three hints on a puzzle. Each one reveals a single letter of a shortest route, not the whole next word, so the rest of the ladder is still yours to work out.
Are the puzzles generated at random?
No. We build them from the fixed graph and a shortest-path search, then pick pairs whose par and route we are happy with. Random letter changes would often produce steps that are obscure or outside the list.
Play today’s ladder → one puzzle a day, about two minutes.