Danish Crossword Puzzles

Most languages on this site were seeded with open lattice grids — the British shape, where long entries cross only at every other square — because a dense, fully checked American grid could not be filled from a pool of common words, and the three that did get dense grids (French, Spanish, Portuguese) got them only at 13×13 and below. Danish is the first shelf where every puzzle is the dense kind, up to the full 15×15: numbered squares, every letter crossed both ways, an Across and a Down list. If you solve the New York Times or the Los Angeles Times, the layout will need no introduction; if you solve Danish magazines, it may, because the kryds og tværs you find on a Danish newsstand usually prints its clues inside the dark squares with small arrows, and has no clue list at all.

What made the dense grid possible was not the size of the vocabulary but the rule for admitting short words. The seeded pools had always held three- and four-letter answers to a higher bar than the rest, and that bar is exactly what a dense grid cannot afford: a 15×15 spends about twenty of its entries at three letters and thirty at four. Lowering it for the American grids — while keeping every other filter, and preferring the most frequent words first — was enough for Danish 15×15s to fill in seconds. Two grid sizes still refused: the stored 7×7 and 9×9 patterns are almost nothing but three-letter crossings, and filled none of four attempts at any floor, so the shelf starts at 11×11.

Danish writes with 29 letters, the Latin 26 and then Æ, Ø and Å, in that order. Each takes its own square and has to be typed as itself, and only Å has a look-alike to trip over: the answer pool holds MAS (bother) beside MÅS, VADE (a mudflat) beside VÅDE, and UDAD (outward) beside UDÅD (a misdeed). Æ and Ø have no plain twin, so nothing in a grid is ever a mistyped E or O.

Å is also the newest letter. Until the spelling reform of 1948 the same sound was written AA, and the old form survives in proper names to this day: Aalborg kept its double A, and Aarhus, having switched to Århus, switched back in 2011. In a grid that matters, because AA is two squares and Å is one — an answer spelled the old way is a different length from the same word spelled the new way. The puzzles here use Å, as the dictionary does; the double-A names are the exception a solver should expect to see clued as such.

As in Norwegian, the definite article lives on the end of the noun — HUS, HUSET, HUSENE — and a dictionary that lists every one of those forms as an entry will happily fill a grid with them. English Wiktionary does: 11,853 Danish headwords in the frequent part of the list are nothing but inflected forms, against 24,619 base forms. The answers here were cut back to the base forms before any grid was filled, so what you write in is hus, not huset.

Because Æ, Ø and Å all sit inside the one-byte Latin-1 encoding, .puz export works for Danish: a puzzle survives the round trip and opens in Across Lite.

Auto-fill draws on about 366,000 Danish entries. Danish compounds the way its neighbours do — børnehave, køleskab, midnatssol, all written as one word — so the list is thick through the middle: nearly 43,800 entries at eight letters, 42,500 at seven, 41,800 at nine, and still 10,000 at fifteen. Norwegian's list, built the same way, peaks at ten letters and is half as large again at every long length; the Danish corpus is simply smaller, and its weight sits where an American grid spends most of its squares.

That shape is what let the dense grid work here where it had not elsewhere. With the short-word bar relaxed, the pool the puzzles were filled from holds 570 three-letter and 1,405 four-letter answers, and nine of the ten grids filled from the most frequent 15% of the vocabulary alone; one 15×15 reached to the top 30%. A third 15×15 could not be filled at all, because each finished grid withholds its sixty to ninety answers from the next and the short end of the pool has no depth to spare — which is why there are two 15×15s on this shelf and five 13×13s.