20×20 Nonogram Puzzles

Twenty is where a nonogram becomes an evening rather than a break, and where most of the larger half of the catalog lives — only a pair of 30×30 boards sit above it. Nearly all of the bucket is true 20×20; the rectangles are the exception, three at 15×20, three at 20×10, and one each at 10×20 and 20×15. A full 20×20 holds four hundred cells — sixteen times a 5×5, and nearly twice a 15×15 — and no amount of staring will get you through one by inspection.

There is a specific reason these feel different, and it is the same arithmetic that governs every other size, pushed past its useful range. A clue of k in a line of n cells forces 2k − n cells. On a ten-cell line a clue of 8 gives you six cells for free. On a fifteen-cell line the same clue gives you one. On a twenty-cell line it gives you nothing at all: you need a clue of 11 before overlap forces even two cells, and clues that large are uncommon. The technique that opens a 10×10 is effectively dead here. What replaces it is cross-referencing — using what a row tells you to constrain a column, then reading that back into the next row — plus the discipline of marking empty cells as deliberately as you mark filled ones, because on a board this size the blanks carry as much information as the blocks.

A minority of the bucket is rated hard, and almost all of those are true 20×20s, so shape and difficulty travel closely together at this size. The theme you pick matters just as much. Every everyday objects board at this size is rated hard, and so is every alchemy piece. Food & drink and hats & masks are both well represented here and pull in opposite directions: hard boards are the exception in the first and common in the second. Animals sits entirely at normal.

That makes animals the way in. A set of large boards, none of them rated hard, and subjects whose outlines you can half-predict from the clues — a useful property when the grid is big enough that a wrong guess costs you real time. From there, food & drink offers the most volume at this size, and everyday objects and alchemy are worth saving until cross-referencing is genuinely automatic rather than something you have to remember to do.

The eight rectangular boards deserve a word of their own. In the 20×10 and 20×15 pieces the columns are the short axis and therefore the one that pays out first; in the 10×20 and 15×20 pieces it is the rows. Working out which axis is shorter before you start is a small habit that saves a disproportionate amount of time at this size.

If this is a step too far, the 15×15 bucket is where the same techniques are required but forgiving, and it holds roughly half the catalog.