How to choose the words for a word search

How many words fit each grid size, why a word needs at least three letters, and the list mistake that makes the printed answer key wrong.

The number of words is set by the grid, not by the topic. A 7x7 grid takes five to eight short words, a 10x10 takes eight to twelve, a 15x15 takes twelve to twenty, and a 20x20 takes eighteen to twenty-five. Our generator aims for 30 cells in every 100 to carry a word letter on the easy setting and 58 in 100 on the hardest one, which is why the same list comes back as a smaller grid when you raise the difficulty. Go over that and the placement stops converging: you get a grid that took ten attempts and still has an empty corner.

The longest word sets the floor. A twelve letter word does not fit in a 10x10 grid in any direction, with any random seed, so the grid has to grow to at least 12x12 before anything else can be decided. The ceiling is paper rather than arithmetic: past about 32 cells a side, an A4 sheet gives cells under 5 mm and the letters stop being readable. One very long word among ten short ones therefore costs you the whole sheet, because the grid grows for that word alone and the rest float in filler.

Under three letters a word cannot hide, and the reason is arithmetic rather than taste. A 15x15 grid contains roughly 1,500 two letter readings across the eight directions, against 676 possible letter pairs, so a two letter word turns up about twice by pure accident wherever you put it. At three letters the count is around 1,560 readings against 17,576 combinations, near 9 per cent, which is rare enough to work with. That is why OX and GO get dropped from a list and CAT does not.

The mistake that ruins a sheet is a word contained in another one. Put CAT and CATTLE on the same list and every possible grid contains CAT twice: once inside CATTLE, and once where CAT itself was placed. The child who circles the CAT inside CATTLE is right, and the answer key you printed says otherwise. No grid can fix this, because the fault is in the list: drop one of the two, or change CAT to CATS or to KITTEN.

The same trap works backwards, and that one nobody spots. STOP and POTS do not contain each other in reading order, but a grid holding STOP holds POTS read from the other end, and the answer key has to be checked in all eight directions no matter which difficulty was set. DOG and GOD, STAR and RATS, PART and TRAP, LIVED and DEVIL all behave the same way. Reverse each short word in your head and read the list again.

Palindromes are the exception, and they are safe. LEVEL placed once reads the same forwards and backwards over the same five cells, so on the answer sheet it is one pencil line and not two. NOON, RADAR, KAYAK, CIVIC and MADAM all behave normally. A tool that counts readings instead of counting cells rejects them and then fails without saying why, which is worth knowing if another generator has refused your list.

Spaces and accents disappear on the way into the grid. ICE CREAM becomes ICECREAM and takes eight cells in a row; there is no way to put a space into a letter grid without telling the solver where the word breaks. CAFE loses its accent for a sharper reason: if the accented letter stayed, it would be the only rare character in a field of random filler, and it would advertise the start of the word from across the room. The readable spelling survives in the word list printed under the grid, which is where it is useful.

The check before you print takes a minute. Sort the list from shortest to longest, then take the three or four shortest words and ask whether each one appears inside any of the others, forwards or backwards. For twenty words that is about sixty comparisons rather than four hundred, because only a short word can hide inside a long one. Our generator refuses a list of this kind and names both words, but most tools do not, and a duplicate found on paper on Monday morning is found in front of the class.