Hidden pair practice sheets
Two digits with only two homes in a unit. The cells look ordinary, which is exactly why this one gets missed.
The pair you cannot see by looking at the cells
A naked pair announces itself: two cells, the same two digits, nothing else. A hidden pair does the opposite. The two cells that make it usually carry four or five candidates each, so nothing about them looks special. What is special is somewhere else — in how two digits are distributed across the whole unit.
That is the whole difficulty. You will not find a hidden pair by staring at a cell. You find it by counting where two particular digits can still go, and noticing that they have been squeezed into the same two cells.
Spotting one, in order
- Pick one unit — a row, a column or a box — and work that unit alone. Hidden pairs are almost always missed because the eye jumps between units.
- Count homes for one digit. How many empty cells in this unit can still take a 3? If it is more than two, this digit is not part of a hidden pair here. Move on.
- Find a second digit with the same two homes. This is the pattern: two digits, exactly two possible cells each, and the same two cells for both.
- Those two cells now hold only those two digits. Cross out every other candidate in them. A cell that showed 2, 5, 7, 9 becomes 2, 5.
Step 4 is where the technique pays. The two digits were always going to sit in those two cells in some order; everything else in those cells was never possible, it just had not been ruled out yet.
One thing worth noticing: after you clear them, those two cells usually become a naked pair. That is not a coincidence — it is the same fact, seen from the other side. Hidden and naked are two ways of describing one arrangement, and clearing a hidden pair is what turns it into the visible kind.
What the grader guarantees
Every puzzle on this sheet needs at least one hidden pair, and nothing on it asks for more than one tier above: the hardest extra step you can meet is an X-Wing or a single-digit colouring. The filter never relaxes to fill a sheet, so if one ever comes up short, press New set — that is the filter refusing to hand you the wrong kind of puzzle.
Printing it
Set scale to 100% ("Actual size" in some browsers; "fit to page" thins the box lines). Four puzzles per page gives 78 mm boards, a classroom handout; two per page leaves room to write pencil marks; one per page fills most of the sheet.
Turn on Candidate marks for this one. A hidden pair is invisible without them: the technique is about which cells can hold a digit, and that information lives entirely in the marks. Working this sheet without marks is a memory exercise, not a pattern exercise. Answer page puts the solutions on separate sheets at the end, numbered to match.
If a puzzle refuses to open
When you are stuck, do not scan the whole grid. Take one digit you have not placed many times and trace it unit by unit — a digit with only two homes somewhere is the entry point, and the second digit usually turns up in the same unit within a minute.
The full guide to hidden pairs works through a position where clearing the pair is the only move available, and sets it beside the naked pair so the two stop blurring together. If the naked version is still shaky, the naked pair sheet is the one to drill first; when pairs of either kind come easily, pointing pairs is the next thing that stops people on medium puzzles.