Naked pairs and hidden pairs: two cells, two digits
Updated
Two cells in a row have exactly the same two candidates. Other cells may still list those digits, but these two cells have reserved them. You can cross them off the rest of the row. The same lock works in a column or a box.
The naked form is the one you see first, once the notes are honest: both cells list those two digits and nothing else. A hidden pair takes a little more looking. The two digits have only two homes, even though both cells still list other candidates. Both are Medium. This page puts them on separate boards, so the two shapes do not sit on top of each other.
A triple is the three-digit version of the same idea. When a triple is the highest step the grading ladder uses to finish a puzzle, Calmtile calls it Hard. The definition is on the difficulty page.
When to use them
After naked singles and hidden singles, and only when you trust the notes. A missing candidate can invent a naked pair. An extra one can hide a real pair. Before deleting anything, check both lists against the row, column, and box. For a hidden pair, check every possible home of the two digits in the house as well. If the lists feel shaky, go back to notes before you delete anything.
Naked pair
Find two cells in one house whose lists are exactly the same two digits. Those cells will be those digits, in one order or the other. No other cell in the house can be either digit. Delete the two digits from the rest of the house. Do not fill either cell yet.
On the first board, r1c1 and r1c2 each allow only 2 and 3. Row 1 already contains 4, 5, 6, 7, and 8. Column 1 contains 1 and 9, at r8c1 and r4c1. Column 2 contains 1 and 9, at r6c2 and r7c2. That is why the two cells are down to 2 and 3.
r1c3 still allows 1, 2, 3, and 9. It does not see either 9, so 9 is still legal, and so is 1. The pair takes 2 and 3 off r1c3, and off r1c4, which has the same list. r1c3 keeps 1 and 9. Stop there. The pair does not choose between 1 and 9, and it does not type a digit. A later single might.
r1c1 and r1c2 are only 2 and 3. Those two digits come off the other open cells in the row.
Hidden pair
Now watch the digits, not the shape of the lists. In row 2 of the second board, 4 can sit only in r2c2 and r2c3. Those same two cells are the only homes for 5. Column 1 is one of the fences: it already holds a 4 at r9c1 and a 5 at r4c1, so r2c1 is closed to both. The other cells of the row are closed the same way, or they are filled, as r2c6 and r2c7 are.
r2c2 and r2c3 are not a naked pair. Each still allows 2, 4, 5, and 7. Because 4 and 5 have no other home in the row, the extras cannot stay. Delete 2 and 7 from both cells. They become 4 and 5, and you still do not know which cell gets 4. The step only tidies the two lists.
4 and 5 appear only in r2c2 and r2c3. The 2 and the 7 come off those two cells.
The step
- Naked: two cells, the same two digits, nothing else. Delete those digits elsewhere in the house.
- Hidden: two digits that share exactly two cells. Delete every other candidate from those cells.
- Stop. A cell that is now a single belongs to the next pass, not to this one.
Easy to misread
Two cells that both contain 2 and 3, plus anything else, are not a naked pair. The lists have to be exactly those two digits. A real third candidate means the cells are not locked. I have deleted from a pair that still had a third digit. The grid did not thank me.
A hidden pair is not “the cell looks busy, so skip it.” The busy list is what you trim. And a pair never fills a cell by itself. Guessing which digit goes where means you have left the technique.
The three-cell version is a triple. It makes a puzzle Hard only when it is the highest step the grading ladder uses to finish the grid. The definition sits on the difficulty page.
Next
Next time two cells keep the same short list, try deleting from the rest of the house before you choose between them. The other Medium check is pointing and box-line reduction.