5×5 Pentadoku is a small Sudoku variant: the grid is divided into five irregular regions, each made of five edge-connected cells. Every row, every column and every region must contain the digits 1 to 5 exactly once. In the interactive lab you can solve puzzles, inspect possible digits and draw your own regions.
The three rules
A digit cannot repeat within a row, column or region. Regions may have different shapes: each must contain exactly five cells connected along their edges. Two cells touching only at a corner are not connected.
An example before you play
Here is one complete grid. Letters identify regions; the number is the digit in that cell. Check it row by row, column by column and region by region.
A1 B2 B3 B4 B5 A2 A3 A4 A5 B1 C3 C4 D5 D1 D2 E4 C5 C1 C2 D3 E5 E1 E2 E3 D4
Region A, for instance, contains 1, 2, 3, 4, 5; so does the first row. If a puzzle’s first row shows 1, 2, 3, 4 and one empty cell, that cell must be 5. This is a deduction, not a guess.
How to reason about a cell
For an empty cell, exclude digits already present in its row, column and region. If only one remains, place it. Also look for a digit that can occupy only one cell in a particular row, column or region: that position is forced. If these checks are not enough, test an assumption and see whether it leads to a contradiction; do not describe a digit copied from the solution as a deduction.
Why the solution must be unique
A correctly completed grid satisfies all three rules, but a puzzle with too few clues may have multiple solutions. The lab offers twelve puzzles checked with a solver: each has exactly one solution. In Build mode you can colour regions and enter clues; the checker distinguishes no solution, one solution and multiple solutions.
The mathematical connection
The row and column conditions form a Latin square of order 5. The regions add a third constraint. A set of five edge-connected cells is a pentomino; here five pentominoes tile the grid without overlaps. Solving Pentadoku means finding a digit assignment that satisfies all these constraints at once.
Try the lab
Open Pentadoku online. In Play mode, choose a puzzle and fill the grid. Hint first looks for a logical move and explicitly says when it instead reveals a solution digit. In Explore, select a cell to see its candidates. In Build, draw five connected regions and check how many solutions your clues allow.