Word Scramble

You are shown the letters of a hidden word in the wrong order and you type a word that uses every one of them, exactly once. Not some of them — all of them, with duplicates respected: a set holding one E will not accept a word wanting two. Solve it and the round's points are the word's length plus whatever is left on the clock. Rounds get one letter longer each time, so a game is a ladder rather than a list.

The part most versions get wrong is what happens when you find a different right answer. A scramble is a bag of letters, and a bag of letters does not know which word it came from. Type SPEAR into a puzzle that chose SPARE and you have solved it; being told you are wrong is the fastest way to be told you are playing something broken. Here every real word built from the exact letters scores the same, and the rest are listed when the round ends.

Constantly, and much more often than players expect. Measured across the 25,322 everyday words this game draws answers from, checked against all 172,823 words it will accept, 55% of four-letter answers have at least one other valid arrangement. The share falls as words get longer, because long letter-bags are far more specific.

The right-hand column is the one that matters at the keyboard: it counts only alternatives that are themselves everyday words, so a four-letter round has a better than one-in-three chance that a second familiar answer exists. The largest families in the shipped list are worth knowing because they turn up often — A E P R S spells twelve words, A E L R S T eleven, and A E S T eight.

• A E P R S — spare, spear, pears, parse, pares, rapes, reaps, apers, apres, asper, prase, presa.
• A E L R S T — alerts, alters, slater, salter, staler, artels, estral, laster, ratels, stelar, talers.
• A E I N R S T — retains, retinas, nastier, stainer, antsier, ratines, retsina, stearin, anestri.
• A E S T — east, eats, etas, sate, seat, seta, teas, ates.

Stop trying to see the word. Build the ending first, then the beginning, and let the middle fall out — English is far more predictable at its edges than in its centre. Of the everyday four-to-eight-letter words in this list, 22.3% end in S, 9.6% end in -ED and 7.7% end in -ING, so three endings account for very nearly four words in ten before you have looked at a single letter in the middle.

• Park the S, then check yourself. It is the commonest opening letter here (13.5% of words) and the commonest ending (22.3%), and 67.8% of every S in this list sits at one edge or the other. Try both ends first — then remember that a quarter of S-words keep their only S in the middle (ISLAND, BASKET, CASTLE) before you decide the rack is broken.
• Look for -ING, -ED, -ER, -LY, -ION. If you can see an I, an N and a G, try them together at the back before you try anything else.
• Keep digraphs married. TH, CH, SH, PH, CK, QU and NG behave as single letters. A Q is decisive: of 172,823 accepted words, only 29 hold a Q that is not immediately followed by a U, and just 21 hold a Q with no U anywhere at all.
• Count the vowels. Two vowels in a five-letter set is C-V-C-V-C — vowels second and fourth — 39.2% of the time, more than any other shape by a distance. Three vowels in a six-letter set puts two of them side by side 67.1% of the time, and that pair is the thing to place first.
• Shake the letters. Being stuck is almost always being stuck on an ordering you have read twenty times. Re-ordering the display costs nothing and is the most reliable unsticking move there is.

Because the search space does not grow, it explodes. Five letters can be arranged 120 ways and a patient player can genuinely read most of them; eight letters can be arranged 40,320 ways, which nobody reads. Repeated letters cut that back — and long words repeat letters far more often, which is the one thing working in your favour.

So four in five eight-letter answers contain a repeat, which halves the real arrangements. Be careful what you do with that, though: a repeat is two of the same letter somewhere, and only 22.6% of eight-letter answers put them side by side. When they are adjacent the pair is worth a lot — L, O, E and S account for 53.1% of all doubled pairs here, and 87.9% of pairs sit inside the word rather than closing it, which pins two positions at once. Seeing two of the same letter is a hint; assuming they are next to each other is not.

Length pays and speed pays. A solved round is worth ten points per letter plus two points for every whole second left on that round's clock, minus fifteen for each hint taken. A skipped round and a round that runs out of time are both worth nothing, and the difference between them is only what the summary calls it.

Notice how much of that total is the clock rather than the letters: 256 of the 446 points came from seconds. A player who solves every round slowly scores less than one who solves four of them fast, which is deliberate — a scramble you eventually get is not the same achievement as a scramble you see.