ABCD

You’re given an empty grid, and several rows of numbers on the side. You have to write a letter in every empty cell, following these rules:

  1. The numbers on the edge indicate how many instances of a specific letter appear in that row or column.
  2. Identical letters cannot be horizontally or vertically adjacent.

One setting adds to the second rule, and a board’s name in the Type menu says when it is on:

Controls

On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click). A key the puzzle’s controls show as a button can be pressed there instead of on a keyboard.

Left-click to select a cell, then type a letter on your keyboard to enter it. Press Backspace or Space to clear a cell.

Right-click a cell, then type a letter to add a pencil mark. Pencil marks can be used for any purpose. Pencil mode is sticky: once a right-click switches it on, it stays on wherever you click, until you right-click again. The Marks key is lit while it is on, and pressing the key also switches it. To have it last only until your next click, turn off Right-click toggles a sticky pencil mode (stays on until right-clicked again) in the preferences.

You can also use the arrow keys to move the selected cell around. Press Enter to toggle between entering letters and entering pencil marks.

Press Fill marks among the puzzle’s controls to write in every pencil mark wherever nothing is placed and no mark is written yet. The M key does the same, on any board where M is not something you type. Marks you have narrowed are left alone, and pressing again never starts over: see Filling in all the pencil marks. Once every empty cell has marks, the press crosses out a letter where a neighboring cell already holds it, and where its row or column already has as many as its clue asks for.

Where the puzzle comes from

The inventor of this type is unknown. This puzzle is also known under the names ABCD Puzzle, ABC-Kombi or ABCD-Rätsel.

More information: https://www.janko.at/Raetsel/Abc-Kombi/index.htm

Hints

Hint explains the next step rather than simply making it. It starts by filling in every cell’s pencil marks (the same as pressing Fill marks), then works from your own marks, so as long as none of them has crossed out a cell’s answer it carries on from wherever you are. If you would rather it leave a cell unmarked until a step needs it, set Hints pencil in to Only as needed in the preferences: a cell with no marks then counts as holding every letter not already beside it.

Most steps are the plain rules at work: a cell with only one pencil mark left, a letter crossed out beside the same letter, or a row that already holds as many of a letter as its number says. One idea goes further. Since no two of the same letter may touch, a stretch of empty cells can hold at most every other cell’s worth: 3 in a stretch of 5, 1 in a stretch of 2. When the stretches of a row that can take a letter hold at most exactly as many as the row still needs, every stretch must be full, and a full stretch of odd length has only one shape: that letter in its first cell, its last, and every other cell between.

On an Unreasonable board there comes a point where none of these settles another cell, and the hint says that nothing further follows by deduction instead of choosing for you. On some boards that is the very first step. Save your position, try a letter, and it carries on from whatever you enter.

ABCD parameters

These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.

Width, Height
Size of the grid in squares (excluding the size of the numbers on the edge). A large board takes longer to find, the more so with more letters, because each extra letter is another count every row and column has to satisfy: with three letters a board of about 130 squares comes in seconds, with four about 80, and from six letters up about 65. Long thin boards go much further, because a short row is almost settled by its own numbers. Past those sizes the first board can take a minute or two to appear, or not be found at all. Each must be at least 2.
Letters
The amount of different letters that can appear in the puzzle. Without diagonal touching there must be at least 5. It must be between 3 and 9.
Difficulty
Determine the difficulty of the generated puzzle; see what the names mean. An Easy puzzle can be finished by the rules alone: there is always a number that settles a letter or rules one out. An Unreasonable one has a single solution that the numbers do not lead to step by step, so somewhere you have to try a letter and see what follows, and the Hint button stops where the rules do.
Remove clues
When enabled, some of the number clues are hidden: as many as can go while the puzzle still has one solution at its difficulty. An Easy puzzle stays one the rules alone finish, with less to read them from.
Allow diagonal touching
When off, identical letters cannot be diagonally adjacent either. Counter-intuitively this raises the size limit described above rather than lowering it: the extra restriction gives you more to reason from, so larger boards still work out to a single solution.

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