How to solve a murder sudoku, step by step
A real case solved from start to finish, with every deduction explained. Includes the trick for naming the murderer before you have placed anybody.
The best way to learn these puzzles is not reading a list of techniques, it is watching a whole case taken apart. So let us solve a real one, from the game page, without skipping a step.
At the end there is a trick almost nobody uses that, in this particular case, lets you name the murderer without having placed a single suspect. It is worth getting that far.
The case
We are at the Miramar hotel. The Marquis of Tinajas has been found dead in reception.
Here is the floor plan. Each letter is a room, rows are numbered top to bottom and columns left to right:
col1 col2 col3 col4 col5
row1 A A B B B
row2 [A✕] A B B C
row3 D D D B C
row4 D D D E C
row5 D D D E E
A = reception D = the dining room
B = the bar E = the kitchen
C = the lounge [A✕] = the body, in reception
The five suspects:
- Countess Vega
- Captain Losada
- Duarte the pianist
- Peralta the tailor
- Bermejo the notary
And the five clues:
- Countess Vega was in column 3.
- Captain Losada was in column 4.
- Peralta the tailor was in the bar.
- Duarte the pianist was in row 3.
- Captain Losada was in row 5.
Remember the two rules: one per row and one per column, and the murderer is the only person left alone with the victim in their room.
Step 1: what comes free
Clues 2 and 5 are about the same person and each gives one coordinate. Column 4 and row 5.
Captain Losada is in row 5, column 4. Placed, without thinking.
This is the first thing to look for, always: two clues about the same person that cross. It is the only way to pin a cell without deducing anything.
Step 2: what Losada has just eliminated
Here is the step most people skip. Placing someone is not only placing someone: it blocks a row and a column for everyone else.
Losada occupies row 5 and column 4. So from now on, nobody else can be in row 5 or in column 4.
Applied to clue 3, Peralta the tailor is in the bar. The bar is six cells: r1c3, r1c4, r1c5, r2c3, r2c4 and r3c4. But three of them are in column 4. Out.
Peralta can only be in r1c3, r1c5 or r2c3.
Step 3: the murderer trick
Now, before placing anybody else, let us look at who could be the culprit. The rule says exactly one person ends up in the room with the body, and that person is the murderer.
Reception is four cells: r1c1, r1c2, r2c1 and r2c2. The body occupies r2c1, so three candidates remain: r1c1, r1c2 and r2c2. All of them are in columns 1 and 2, and in rows 1 and 2.
One by one:
- Losada is in r5c4. No.
- Vega is in column 3 (clue 1). Reception has no cells in column 3. No.
- Peralta is in the bar (clue 3), which is a different room. No.
- Duarte is in row 3 (clue 4). Reception does not reach row 3. No.
- Bermejo: no clue excludes him.
Somebody has to be in reception, because the rule demands it. And the other four cannot.
The murderer is Bermejo the notary. And we have not placed anyone except Losada.
This reasoning — «do not ask me where each person is, ask me who can be here» — is the highest-yield move in the format and the least used. Note that no clue about Bermejo was needed at all: he is identified by eliminating the other four.
Step 4: closing the board
We know the culprit, but the puzzle is not solved until everyone has their cell. And from here it runs smoothly.
Available rows: Losada occupies row 5. That leaves rows 1, 2, 3 and 4 for Vega, Duarte, Peralta and Bermejo. Duarte is in row 3 (clue 4), so Vega, Peralta and Bermejo share rows 1, 2 and 4.
- Bermejo is in reception, so r1c1, r1c2 or r2c2: rows 1 or 2.
- Peralta is in r1c3, r1c5 or r2c3: rows 1 or 2 as well.
Between them they take rows 1 and 2. Therefore:
Countess Vega is in row 4. And since clue 1 puts her in column 3: Vega is in r4c3.
With column 3 now taken by Vega, Peralta loses two of his three options (r1c3 and r2c3). Only one remains:
Peralta the tailor is in r1c5.
Peralta takes row 1, so Bermejo gets row 2. Of his three possible cells, r1c1 and r1c2 are in row 1. One remains:
Bermejo the notary is in r2c2 — right beside the body, in reception. Which fits what we already knew.
And for Duarte, who is in row 3: columns 2, 3, 4 and 5 are already taken by Bermejo, Vega, Losada and Peralta. Only column 1 is left:
Duarte the pianist is in r3c1.
The solution
col1 col2 col3 col4 col5
row1 Peralta
row2 BERMEJO
row3 Duarte
row4 Vega
row5 Losada
The body: row 2, column 1 (reception)
The murderer: Bermejo the notary, the only one in reception
Five clues, five deductions, no guesswork. Check that no two people share a row or a column: rows 1, 2, 3, 4, 5 and columns 5, 2, 1, 3, 4. Correct.
What to take away from this
Four ideas, in order of usefulness:
- Look for crossings first. Two clues about the same person giving a row and a column are a free cell.
- After every placement, review. The row and column you just blocked usually knock out possibilities for another two or three people.
- Ask it backwards. Instead of «where is this person», try «who can be in this room». That is what solved the culprit in step 3.
- Never guess. In a well-built case you do not need to. If you find yourself trying options, there is a deduction you have not seen — usually the one in point 3.
To practise
- Free cases in your browser, in three levels. It highlights the legal cells as you place, so the board itself enforces the row-and-column rule.
- Printable cases, six per sheet with the solutions at the end.
- And if you want the background on where this format comes from, it is in what a murdoku is.