zedoku

hidden single

level 2 - easy

a number can only go in one cell of a row, column, or box—even though that cell has other candidates too.

what it means

sometimes a number appears as a candidate in multiple empty cells. but when you look at the whole row, column, or box, you realize that only one of those cells can actually contain that number. the number is "hidden" among other candidates in that cell.

the "kids and toys" analogy

imagine three kids who all want the same toy. but there's a rule: only one kid can have it. even though all three kids asked for it, you look at the rules and realize only one of them is actually allowed to have it.

in sudoku, the number 8 might be a candidate in three different cells. but when you check the rows and columns, you find that only one of those cells can actually be 8. that cell has a hidden single!

example 1: finding 8 in a box

look at this 3×3 box. we need to place the number 8. let's see where it can go:

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1
2
3
Empty
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4
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9
5
Empty
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6
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only one cell can be 8

the center cell is the only empty spot in this box. all other cells already have numbers (1, 2, 3, 4, 5, 6, 7, 9). so the center cell must be 8!

example 2: hidden among other candidates

now look at this trickier situation. multiple cells show 8 as a possible candidate:

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1
2
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Empty
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4
1
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5
Empty
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6
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9
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three cells have 8 as a candidate

wait! we need to check the rows and columns that pass through this box:

  • the left cell is in a row that already has 8 somewhere else
  • the right cell is in a column that already has 8 somewhere else
  • only the center cell can actually be 8!

example 3: before and after

here's how the grid looks before and after finding the hidden single:

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1
2
3
Empty
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4
1
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4
5
6
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5
Empty
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before: 8 is hidden among candidates

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1
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Empty
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4
8
5
Empty
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6
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9
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after: 8 is placed!

even though the center cell had other candidates (8 was just one possibility), it was the only cell in the box that could actually contain 8. that makes it a hidden single!

example 4: hidden single in a row

hidden singles can appear in rows and columns too. look at this row:

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3
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7
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1
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only one cell can be 9 in this row

the row needs 6, 8, and 9. but look at the boxes these empty cells belong to:

  • the middle cells' boxes already contain 9
  • only the left cell can actually be 9!

key insight

the key to finding hidden singles is to look at each number (1-9) and ask: "in this row, column, or box, how many cells can actually contain this number?"

if the answer is exactly one, you've found a hidden single!

when to use this technique

  • when you've filled in all the obvious candidates
  • when no cell has only one candidate left (that would be an obvious single)
  • when you need to look deeper at where each number can go in a unit

tips for spotting hidden singles

  • scan each box, row, and column for each number from 1 to 9
  • if a number already exists in a unit, you can skip it
  • cross out cells that can't contain the number due to conflicts
  • if only one cell remains, that's your hidden single!
back to tutorialnext: obvious pairs