Solve 6x6 grid puzzle without guessing, one step at a time
Learn to solve 6x6 grid puzzle without guessing: check each 2x3 region, row and column, and cross out digits until every cell has one answer.
Suppose the third row of a 6×6 grid already holds the numbers 2, 5, 1, and 6, with two empty cells left near the center. A beginner looks at those two cells and sees that both 3 and 4 are missing, so the right placement cannot be decided yet. As a trial, the player writes a 3 in one of the two cells. The 3 stays if the other cells can still be filled in correctly. When a conflict shows up later, the player erases several numbers and begins the process over.
Players often put in trial numbers on small grids, since the board looks simple enough to test ideas quickly. Under that rule, each of the digits 1 to 6 appears exactly once in every row, every column and every marked 2 × 3 region.
A solver needs nothing beyond that rule. Every filled cell takes one digit away from the cells in its row, column or region, and before making any pencil mark, the solver can check the empty cells in a row against all three groups.
Start with the 2x3 regions
The solver begins with one marked 2×3 region and writes down which digits from one to six are still missing. If the top left region already holds 1, 3, 4, and 6, for example, the digits 2 and 5 are missing and two cells are still open. The solver does not try to put either digit into a cell at this stage. The solver only holds the short list of possible digits in mind.
Next, the solver checks the surroundings of each empty square. Suppose the top square of a pair sits in a row that already has a 2 farther along. That row cannot hold a second 2, so the square cannot be a 2. Within the region, the player takes 2 off the list of possible numbers for that square.
Just one square is left that can take the number two. The two is placed in that square, and the first square has to hold the five. The solver made no guess, and nothing had to be erased.
Solvers go through all six regions one after another, since a short list of two or three missing digits gives the row and column checks the most to work with.
Check rows and columns for forced numbers
Next the solver picks a row and counts its empty spots, and if the row holds two numbers, the solver lists the four digits that are missing. Beside the row, the solver writes the four digits, such as 1, 3, 4 and 6, and then checks which of them each open cell can still hold.
The solver compares each open cell with its own column and its own region. A cell whose column already has a 4 gets crossed off for the 4. Another cell is crossed off as well when a 4 in its region blocks it. Once only one cell in the row can still take the 4, the 4 goes in that cell, even if the cell could also accept other digits.
Solvers use the same method on each column and count the digits that column still needs.
Once a cell has been lightly marked with a dot or faint pencil mark, the solver looks at the column again. The new number eliminates one possible digit from each remaining empty cell in that column and can force another cell in that column.
Stop when a cell has one option
When a solver does not use trial and error, they make a small list of possible numbers for each empty cell. In a cell that can contain any number from one to six, the list starts with 1, 2, 3, 4, 5, 6. The solver then checks the row, the column, and the 2‑by‑3 region that the cell belongs to, eliminating any number that appears in any of those three areas. Say the row already has a 2, the column has a 5, and the region has a 1 and a 6. Then only 3 and 4 are left for that cell.
When a cell's candidate list contains only one digit, that digit is the answer. The solver writes it in pencil or ink without checking it against anything else, because all other digits have already been eliminated by the numbers that appear in the grid.
NumFall is a free iPhone app whose Classic 6x6 set has 100 levels, and every level is built to be solved by logic alone, so this crossing-out method is enough for each one. It is available on the App Store.
After every number is placed, the solver eliminates that number from the possibility lists of all cells in the same row, column and region, and then checks for any list that now contains only one digit.
FAQ
Can you solve a 6x6 grid puzzle without guessing?
When a puzzle is made only with logic, every digit can be determined by eliminating the numbers that are already present in its row, column, or region. Solvers who follow this approach almost never need to change any of their earlier decisions.
What are the rules of a 6x6 number grid?
Every digit from 1 to 6 must appear exactly one time in each row, each column, and each designated 2×3 region.
Where should a beginner start on a 6x6 grid?
Many solvers start with the 2×3 region that contains the most numbers already filled in. A small list of the missing digits is easiest to compare with the rows and columns that surround that region.
How do you know when a number is certain?
A number is known for sure when an empty square has only one possible digit in its list. All the other digits have been eliminated because they are already present in the same row, column, or region.
Is there a free app with 6x6 puzzles that need no guessing?
NumFall is a free iPhone app that contains a Classic 6x6 set of 100 levels, each of which can be solved using logic alone. The app is available on the App Store.
NumFall is made by the publisher of this site. Any health or brain-training points here are general information, not medical advice.