Sudoku Walkthrough: Solving One Puzzle From Start to Finish

How to read this Sudoku walkthrough

Throughout this Sudoku walkthrough, r stands for row and c for column, so r3c7 means row 3, column 7, counting from the top left. Digits 1 to 9 stand in for the nine shapes you would see in Shapedoku, where each number is a distinct glowing symbol. We will start the way every solve should, by looking for cells that already have only one possible answer, then move to slightly harder scans only when the easy wins dry up. The goal is not speed but a clear order of attack you can copy on any grid. Keep a candidate map in your head or in the Notes view as we go, because later steps depend on candidates we uncover early.

Opening: hidden and naked singles

We begin by hunting hidden singles, the friendliest move. Scan box by box for a digit that fits in only one cell of that box. Suppose in box 1 the digit 5 can only go at r1c3, because 5 already sits in the nearby rows and columns; place 5 at r1c3. That placement frees column 3, and now 5 in box 4 is pushed to a single cell at r5c3, so place it too. Next, look for naked singles, cells where eight of the nine digits are already blocked. Say r4c4 sees every digit except 5 across its row, column and box, leaving only 5; write 5 there. Chaining these direct placements, we might fill six or seven cells before the easy supply runs out. Always exhaust singles fully before anything harder, because each one you find can trigger the next.

Middle game: pairs and pointing

When singles stall, switch to candidate trimming. Imagine box 6 has 2 confined to r4c8 and r5c8, both in column 8. That is a pointing pair: 2 can be removed from every other cell of column 8 outside box 6, such as r1c8 and r8c8. Removing those may expose a hidden single elsewhere. Next, look for a naked pair. If r7c1 and r7c4 both hold exactly 3 and 9, and no other cell in row 7 can be 3 or 9 without them, then 3 and 9 are locked to those two cells, so you strike 3 and 9 from the rest of row 7. Suppose that clears r7c6 down to a lone 6; place it. This back and forth between pointing pairs, naked pairs and freshly revealed singles is the engine of the middle game, and on a Medium grid it usually carries you most of the way home.

Endgame: one clean elimination to finish

Near the end, a single sharper move often unlocks the rest. Say 4 remains stubborn, appearing only twice in column c2 at r2c2 and r6c2, and only twice in column c7 at r2c7 and r9c7, with both pairs sharing row r2. That is a skyscraper: one of the far ends, r6c2 or r9c7, must be 4, so any cell seeing both loses 4. If r9c2 sees both ends, remove 4 there, which leaves r9c2 as a naked single 7. From that crack the grid tumbles: the 7 resolves row 9, which resolves box 8, and a cascade of singles fills the final dozen cells. We finish by checking that every row, column and box holds each digit exactly once, the definition of a solved Sudoku. You can practise this exact rhythm in Shapedoku, where the Notes view with smart cleanup keeps your candidate map tidy and the first free hint can explain why a shape belongs in a cell you cannot crack.

1. Fill every hidden single and naked single you can find first.
2. When placements stall, trim candidates with pointing pairs and naked pairs.
3. Re-scan for singles after every elimination, since one unlocks another.
4. Reach for one single-digit pattern, like a skyscraper, to break the endgame.
5. Verify each house contains all nine digits exactly once before you stop.