Every row, column and box gets the digits 1 to 6. Small grid, real logic.
Sahi Sudoku is a free daily logic puzzle played on a 6×6 grid divided into six 3×2 boxes. A new puzzle is generated every day at midnight IST and is the same for everyone, so you can compare your time with a friend who played the same grid.
The rules are the ones you already know from the classic 9×9 game, on a smaller board. Every row must contain the digits 1 to 6 exactly once. Every column must contain the digits 1 to 6 exactly once. Every 3×2 box must contain the digits 1 to 6 exactly once. Some cells are filled in at the start; those are fixed and cannot be changed. The puzzle is finished when every empty cell holds a digit and no rule is broken.
To play, tap a cell to select it and press a number from 1 to 6, or use a keyboard: the arrow keys move between cells, the number keys enter a digit, and Backspace clears one. Cells that break a rule are highlighted as you go, so a mistake is visible immediately rather than twenty moves later.
The smaller grid makes this a good place to learn the reasoning behind Sudoku without the long search a 9×9 board demands. Every puzzle is solvable by deduction alone, so you never need to guess. The two techniques that crack most grids are asking which digits a single cell could possibly hold, and asking where in a row, column or box a particular digit can still go. Those are the same constraint-propagation ideas that scheduling and timetabling software runs on.