Starting a Sudoku Without Guessing

The first ten placements of a sudoku are where most guessing happens. The grid is mostly empty, the eye has no anchor, and the temptation is to try a number and see what happens. Guessing this early almost always wastes time, because the moves that exist are easy to find if you know where to look.

A well-made sudoku from a reputable source has exactly one solution and can be solved by pure logic from the first placement to the last. If you are guessing at move three, you have missed something a methodical scan would have found.

The opening routine

1. 1
   Count the givens for each digit

   Look at the board and notice which digits already appear most often. A digit with seven copies on the board has only two homes left. Start there.
2. 2
   Scan the most-placed digit by box

   Walk the nine boxes. Most-placed digits have very few candidate cells in any given box. Often one box will yield an immediate hidden single.
3. 3
   Place the easy ones first

   Hidden singles in boxes are usually the first three or four moves. Place them in any order you find them. Order does not matter; the moves do not interact much this early.
4. 4
   Re-scan only the digits you placed

   After every placement, scan that digit's row, column and box one more time. New singles appear immediately after every placement.

The rule against speculation

Speculation looks like this: "Let me put a 4 here and see if the puzzle works out". That is guessing. You might be right, you might be wrong, but either way you are not solving the puzzle. You are rolling a die.

The cost of guessing wrong is high. You will fill in five more cells based on the bad assumption before you hit a contradiction. Then you have to figure out which five to erase, which means starting over emotionally even if not literally.

The cost of finding a real placement is lower. It takes thirty more seconds of scanning, and the placement is correct. The cascade that follows is correct too.

The legitimate forms of "if-then"

Some advanced techniques look like guessing but are not. Forcing chains and coloring trace consequences of "if this cell is X" but they only commit when both branches converge or when one branch produces a contradiction. The difference is that the conclusion is logically forced, not assumed.

Beginners should not reach for those techniques. Stick with scans and singles for the first ten placements. By placement eleven, the puzzle has usually loosened up enough that pairs and pointing pairs start to surface.

What to do if a scan finds nothing

First, recheck the scan. Most "nothing here" verdicts are wrong on a second pass. Pick a different digit. Scan boxes you skipped. Once you have honestly scanned every digit by every unit, and still found nothing, you have either reached the pencil-mark stage of the puzzle or, more rarely, you have made an error earlier.

Check the row, column and box of every digit you placed. Find duplicates if there are any. Erase the bad placements and try again. Then, only then, lay down pencil marks.

Why opening calm matters

The first five minutes set the rhythm of the rest of the solve. If you start by guessing, you train your brain to associate sudoku with anxiety. If you start by scanning calmly, you train it to associate sudoku with patience. The puzzle is the same. Your relationship with it is what shifts.

For a slower walkthrough of the technique order, see how to solve sudoku step-by-step. Then try an easy puzzle without guessing once, and see how quickly the cascade builds.