Rung a Day

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Why four letters

Shorter words connect more tightly, which is why most daily ladders are four letters long.

Four letters, many neighbours

A word ladder is a walk through a graph. Each word is a point, and two points are joined when a single letter separates them. Solving a ladder means finding a path between two points, so the shape of the graph decides how hard the search will be. Four letters sits in a useful middle. The graph is dense enough that paths exist between most pairs, yet open enough that finding a short one still takes thought.

Density is the reason. A four-letter word has few positions to change, and the pool of common four-letter words is packed into a small set of possible strings, so a single letter swap stands a good chance of landing on a word you know. Four-letter word graphs are denser than five-letter ones, and a denser graph gives you more legal neighbours at every step. More neighbours mean more routes through, which makes four-letter ladders usually easier and shorter than five-letter ladders.

Why five letters is harder

Add a fifth position and the same puzzle becomes a different job. A five-letter word has more places to vary, but the common five-letter words are spread across a much larger set of possible strings, so the graph thins out. Many promising rungs turn out not to be words in the list, and each dead end costs a step to discover and another to undo. The shortest route between two five-letter words also tends to run longer, which leaves more room for a wrong turn to matter. Five letters is playable, but it asks for patience that four letters does not.

Why three letters is too easy

Three letters sounds like a gentler start, and in one way it is. Short words sit close together, so many pairs are joined within a step or two, and a ladder can be finished before it starts to feel like a puzzle. There is little room to plan, and little to learn from a wrong move. Short forms also sit near names and abbreviations, and those are rejected, which narrows the choices further. A ladder that resolves in a move or two leaves little to solve, so the shortest length is not the friendliest one.

What it means for par

Par is the number of steps in the shortest possible ladder, found by exhaustive search rather than estimated. At four letters that number is usually small, because the dense graph keeps the two ends close together. A small par helps a solver: it is a promise that a route of that length exists, not a guess, and it tells you when a solution is already tight. If par is four and you have used seven, you have not failed. You have found a longer route, and a shorter one is still there.

One puzzle a day

The daily version leans on the same shape. One puzzle a day, the same for everyone, resets at local midnight, and needs no account. Four letters keeps a round short enough to finish in one sitting, and a fixed par gives every solver the same target. Up to three hints are available, and a hint reveals one letter of a shortest route, so a stuck solver can rejoin the short path instead of abandoning it. Rung a Day uses about 2,300 common four-letter English words, with obscure words, dialect words and proper nouns rejected.

Questions

Why are four-letter word ladders usually easier than five-letter ones?

Four-letter word graphs are denser than five-letter ones. Each step has more legal neighbours, so paths between two words are shorter and more numerous. Five-letter words are spread more thinly, which means more dead ends and longer routes, and the puzzle asks more of your patience.

Is a three-letter ladder a good warm-up?

It can be, but there is little puzzle in it. Three-letter words sit close together, so a ladder often resolves in a step or two, and short forms sit near names and abbreviations that are rejected. Four letters give the search enough room to be interesting.

Does density mean four-letter par is always low?

No. Par is the number of steps in the shortest possible ladder, found by exhaustive search rather than estimated, and some four-letter pairs still need several steps. Density makes short routes more likely, not certain, so par is worked out for each puzzle rather than assumed.

How do hints work when par is known?

There are up to three hints per puzzle, and a hint reveals one letter of a shortest route. Because par comes from an exhaustive search, that route is a real minimum. The hint keeps you on a shortest path rather than simply moving you forward.

Play today’s ladder → one puzzle a day, about two minutes.