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How to Solve Fog of War Sudoku: What Should You Reveal First?

Every move in a fog of war Sudoku does two jobs. It fills a cell, and it uncovers part of the board. Ordinary Sudoku only has the first, which is why the ordinary advice runs out here.

This page assumes you know what the fog does; if not, what fog of war Sudoku is covers the mechanic and this picks up from there.

Fog hides constraints and never invents them

Everything below comes out of one lopsided fact. A hidden cell may hold a clue, and if it does, that clue rules digits out of everything sharing its row, column or box. You have no way of knowing. So the candidates you can work out are the digits that nothing visible forbids, and the real candidates are somewhere inside that set.

The fog can only make your list too long. It can never make it too short.

Naked singles come through intact

A cell with one candidate left is safe. The real list sits inside the list you built, and it is not empty, because the cell has an answer. One candidate in, one answer out.

That is worth knowing early, because it means the technique you already have transfers without a footnote. Naked singles work under fog exactly as they work without it.

Hidden singles do not

The middle column is fully clear. You can see all nine of its cells, none of them holds an 8, so its 8 has to go in one of the empty ones. Exactly one of them will take an 8 — and fog could only ever knock more cells out of contention, never put one back, so that cell is the 8. The reasoning holds.

Now the same reasoning on the top row.

Three of its nine cells are out of the fog: a 6 at the left end, an 8 at the right end, and one empty cell between them. Every digit the row appears to be missing therefore has “only one place it can go”, which should be the first sign that something is wrong. Work it for the 4 and you will place a 4 in that gap. There is already a 4 in this row, one cell to the right of it, under the fog.

So the rule to carry: read a unit for hidden singles only when you can see all nine of its cells. How many units that leaves you depends on how the game draws its opening. On the boards in these two articles, which open the way Sudoku Fog does, it is the middle row, the middle column and the centre box, and nothing else.

The first move is not a choice

On the board below, and on the one in the previous article, the opening position offers exactly one move you can prove — a hidden single, in one of those three fully visible units. No naked single exists yet, because every empty cell you can see still has most of its row and box hidden behind grey.

So there is nothing to decide at move one. Find the single unit that pays out and play it.

The choice shows up at move two

Placing that first digit clears ten more cells on the board below. Four provable moves appear at once, and this is where fog of war Sudoku stops resembling Sudoku, because the four are not worth the same:

• r5c2 = 6, a hidden single in the middle row — uncovers 10 new cells.
• r3c4 = 6, a hidden single in the top-middle box — uncovers 4.
• r1c5 = 5, a naked single — uncovers nothing.
• r4c5 = 4, a hidden single in the middle column — uncovers nothing.

All four are correct. Two of them buy you nothing you can see, because every cell they touch is already clear.

Play all four, in that order. A move that opens nothing is not wasted — it still constrains its row, column and box, and it may be what makes the next single appear — but the move that opens ten is the one that changes what you are able to prove next, so it should not sit at the back of the queue.

Notice the third one. r1c5 is that lone empty cell in the top row — the cell the hidden-single argument above put a 4 in. As a naked single it is a 5, and it is safe. Same cell, two arguments, one of them sound.

So: what should you reveal first?

1. Sweep for naked singles and place them. They are always safe, and they are cheap to spot once a unit has a few digits in it.
2. Read the fully visible units for hidden singles. Count the grey cells before you trust one.
3. When several proved moves are waiting, play the one with the most fog around it first. Corners and edges of the clear region pay more than its middle.
4. Repeat. The clear region grows outwards, and units keep crossing from “partly hidden” to “fully visible”, which is when their hidden singles become readable.

Try it

A medium board, which starts with a different opening shape from the easy one in the previous article — the same middle row and column, with the two diagonals cleared as well.

Four ways this goes wrong

Reading a partly fogged unit for hidden singles. The most expensive mistake available here, because the reasoning feels identical to the sound version and produces a confident wrong answer.

Treating auto-filled candidates as facts. Sudoku Fog’s Smart Notes fill in the digits nothing visible forbids, which is the right answer to the question they are asking and not the same thing as the truth. A three-candidate cell may really have one candidate.

Chasing the biggest reveal instead of the proved move. Uncovering a lot of board is worth nothing if the digit was wrong; in the game a wrong digit costs a life and uncovers nothing at all.

Carrying the guarantee into Hardcore. Hardcore mode puts your answers on the board without checking them, so the digits your candidate lists are built from may themselves be wrong. Naked singles are only as safe as the placements they are counted from.

Where to go next

What fog of war Sudoku is has the mechanic and a gentler board. Naked singles and hidden singles is where both techniques come from, and pencil marks is the notation they read. Everything published so far is on the Learn index.

Sudoku Fog is on Android — What Sudoku Fog is, Get it on Google Play.