Dedoku: Deduction Detective

Dedoku: Sudoku’s row-and-column rule, played with witnesses

Dedoku is a logic puzzle built on one rule taken straight from Sudoku: every case piece takes its own row and its own column. Instead of digits, you place a handful of witnesses and one missing item on the floor plan of a building. Clues about rooms, furniture and where people stood tell you who goes where, and the row-and-column rule turns those clues into a finished case.

Every case makes two promises: there is exactly one answer, and you never have to guess. We checked both against the game’s own engine rather than taking them on trust. Of 45 cases generated across the four difficulty levels, all 45 had exactly one answer, and all 45 could be finished by the game’s human-style solver, which only ever removes a square when a clue or the grid rule rules it out.

This page is about the Sudoku half of the puzzle: what that one rule does to the shape of every answer, where in a case it does its work, and why anyone who already solves Sudoku starts a Dedoku case with more of the technique than they realise.

What every Dedoku answer looks like

A Dedoku case always has as many pieces as its map has rows: six pieces on a 6×6 map, ten on a 10×10. With one piece allowed per row and one per column, that means every row and every column ends up holding exactly one piece. No row is left empty and none is shared.

Sudoku players have seen this shape thousands of times without naming it. Take a finished Sudoku and look only at where the 5s are: nine cells, one in every row and every column. A Dedoku answer is that same pattern with the 3×3 boxes taken away and each mark given a name. It belongs to the same family as Queens-style puzzles, which also place one mark per row and column — the difference is that Dedoku’s marks are different people, so the question is never just where, but who.

One more rule shapes the ending. Of all the witnesses, exactly one shares a room with the missing item, and that witness is the one who found it. The generator throws away any case where that is not true, which is why the reveal can always name a single finder.

The rules, exactly as the game checks them

Several of these rules are stricter or looser than they sound, and the difference decides cases. These are the versions the game’s clue checker actually applies:

1. One case piece per row, one per column. The witnesses and the missing item all count.
2. Floor and usable surfaces only. A piece can stand on an open square or on a rug, chair or sofa. Blocked furniture — shelves, display cases, plants and the like — holds nobody.
3. “Beside” means sharing an edge, inside the same room. North, south, east or west, never diagonal. If a wall runs between the two squares they are not beside each other, and standing on an object does not count as standing beside it.
4. “Beside a shelf” means any shelf. A clue names a kind of object, not one particular piece of furniture.
5. Directions are broad. “Felipe was west of Priya” means Felipe is in any column further west than Priya, in any row, in any room. It does not mean directly west.
6. Head counts count people. “Ivy was alone in the Lounge” and “exactly two people were in the Terrace” never include the missing item.

Rule five catches more players than any other. A Sudoku mind reads “west of” as “somewhere along the same row”, which throws away squares that are still perfectly possible.

A Dedoku case, read like a Sudoku grid

The notebook the game gives you is a candidate grid. Where a Sudoku cell carries small digits for what could still go there, a Dedoku square carries the pieces that could still be standing on it. The picture below is a real case from the generator, drawn exactly that way: initials in place of pencil-mark digits, rooms as heavy outlines, furniture as solid blocks.

Read it the way you would read a Sudoku grid part-way through. Most squares still carry two or three names. Nothing is placed yet. But one witness has run out of options, and in a puzzle where every row and every column can only hold one piece, that single fact is about to do a lot more than place one witness.

What the Sudoku rule does when a witness is pinned

Once a piece has only one square left, it owns that square’s entire row and entire column. Nobody else can be anywhere along either of them. That is the same move a Sudoku player makes a hundred times a puzzle: put a 5 in a cell and strike 5 from every other cell in its row and column.

It is worth knowing how much of this the game does for you. When Hint places a witness because a clue has left it one square, it also clears the other notes from that row and column. When you place a witness yourself, the game removes only that witness’s own notes; everyone else’s notes along the row and column stay where you left them until you clear them.

Could you solve Dedoku without the Sudoku rule?

Counted by eliminations, the row-and-column rule looks like a minor part of the puzzle. Across 45 generated cases it removed 14.6% of all the squares the solver ruled out, and clues removed the other 85.4%. But a count treats every removed square as equal. A clue like “Quinn was in the Planetarium” can wipe out dozens of squares at the very start of a case, and that says nothing about whether the case could be finished without the rule.

So we asked the question the count cannot answer. We ran the game’s own solver over 47 cases twice — once as shipped, and once with the row-and-column rule switched off and every clue still available.

Cases generated by the game's own generator, then run through its own human-style solver twice: once exactly as shipped, and once with the two row-and-column rules switched off and every clue still in play. The copied solver was checked against the shipped one on all 47 cases before either result was trusted.

The Sudoku techniques inside the solver

The game’s solver names its reasons as it works, and several of those names come straight from Sudoku. That makes it possible to say exactly which Sudoku techniques do real work in Dedoku, and how much:

Every elimination the game's human solver made across 45 generated cases, 21,799 in all, grouped by the reason it logs. Together the row-and-column rule accounts for 14.6%; clues account for the other 85.4%.

The ranking mirrors Sudoku. The plain sweep after a placement does most of the work, lines already spoken for and hidden singles on a row or column come next, and pairs across lines are rare. If you have ever spotted a hidden single in Sudoku — a digit with only one place left in its row — you already know how to spot a row that only one witness can still use.

The clues that do most of the work

The clues carry most of the eliminations, but not in equal measure. These seven removed the most squares across the same 45 cases:

The seven clue types that removed the most squares across the same 45 cases. The example sentences are rendered by the game itself from real generated cases, so they are worded exactly as a clue card shows them.

Two things stand out. The row and column clues are the most Sudoku-shaped of all — they hand you a line directly. And the two biggest clue types, the room-edge and same-line-as-an-object clues, work by cutting a room down to a single row or column inside it. Either way, many clues end up pinning a witness to a line, which is exactly the form the row-and-column rule can then use.

How the four difficulty levels differ

Difficulty in Dedoku is partly the size of the map and partly the vocabulary of the clues. Bigger maps bring more pieces, more rooms and more furniture, and each level unlocks clue types the one below does not use:

Map ranges and clue-type counts are read from the difficulty profiles in the generator. The last two columns are observed on 47 generated cases, not taken from settings. A case always has as many pieces as its map has rows, which is what lets every row and every column hold exactly one.

Easy sticks to direct clues: a room, a row, a column, a corner, on or beside an object. Medium adds negatives (“Carla was not in the Gallery”), people who were alone, and head counts for a room. Hard brings in compass directions between people and objects and clues about appearance. Expert adds exact offsets between two people, and nine of the eleven Expert cases we generated handed out at least one anonymous tip — a general clue, such as a room’s head count, that is not attached to any one witness.

Bigger cases also take the generator longer to build. An Easy case is ready almost instantly, while a Hard case typically took 20 to 30 seconds to build in our tests, which is why the game prepares the next case in the background while you solve the current one.

Notes, X marks and the buttons

Pick a piece from the case file, then work on the map with one of four modes:

• Smart — tap a square to add or remove a note for the selected piece, and tap a square that already carries its note to place it. This is the one most people leave switched on.
• Note — taps only ever add or remove notes.
• Place — taps place the selected piece straight away. Placing a piece on an occupied square moves the other piece off; tapping a placed piece’s own square picks it back up.
• X — rules a square out entirely and clears its notes; tap it again to lift the mark.

The buttons around the map do different jobs. Check marks any placed piece that is in the wrong square or shares a row or column with another piece, shows which clues are not yet satisfied, and tells you how many pieces are still unplaced. Hint shows the next useful deduction the solver can make — adding the squares a clue allows, trimming notes a clue rules out, or placing a piece when only one square is left. Solve fills in the verified answer, Reset clears the board back to the start of the case, and New Case deals a fresh one at the chosen difficulty.

How to start a case

1. Read the row, column and room clues first. They give the fastest, cleanest cuts and put the most notes in the right places early.
2. Mark every square a clue still allows, not just the likely ones. Dedoku rewards a complete notebook the way Sudoku rewards complete pencil marks.
3. Watch for a witness down to one square. The moment it happens, clear its whole row and column of everyone else.
4. Look along the lines, not just at people. A row that only one witness can still use belongs to that witness, even if they have several squares left in it.
5. Save the head counts for later. “Exactly two people were in the Terrace” does little on an empty map and a great deal once most witnesses are down to a room or two.

The cases are light detective stories — a missing diamond, crown, golden key or trophy rather than anything grim — which makes Dedoku an easy one to share with younger solvers.

Where to go from here

Because the rule at the heart of Dedoku is Sudoku’s own, the fastest way to get quicker at it is to get quicker at Sudoku’s line logic. The Sudoku Trainer drills hidden singles and pairs one technique at a time, and the Sudoku Helper explains the next logical move on any Sudoku position you enter. Our guide to Sudoku techniques covers the rest of the ladder.

If it is the rooms you enjoy, Jigsaw Sudoku swaps the 3×3 boxes for irregular regions much like Dedoku’s floor plans, while keeping every other Sudoku rule.