zedoku

hidden pairs

level 3 - medium

also known as: hidden twins

what it means

two numbers can only go in two specific cells — even though those cells have other candidates too. the pair is hidden among other candidates.

example 1: before — a busy row

look at this row. the cells seem to have many candidates. but look closer — can you spot where numbers 2 and 8 must go?

1
9
4
 2  5  89
6
7
 23   78 
3
5

two cells have multiple candidates — but only they can hold 2 and 8

example 2: analysis — scan for the pair

scan the row: where can 2 go? where can 8 go? look carefully — they can only appear in the same two cells!

where can 2 go?

1
9
4
 2  5  89
6
7
 23   78 
3
5

where can 8 go?

1
9
4
 2  5  89
6
7
 23   78 
3
5

cells 4 and 7 are the only places for both 2 and 8 — they form a hidden pair!

example 3: after — eliminate the extras

since 2 and 8 must occupy those two cells, we can remove all other candidates from them. the hidden pair is revealed!

1
9
4
 2     8 
6
7
 2     8 
3
5
hidden pair [2, 8] revealed

key concept: the secret agents analogy

imagine three secret agents need to hide in a neighborhood. there are five houses, but agents can only hide in three of them (due to security restrictions). the agents are hidden among the possible locations.

now imagine instead: three agents, but only two houses are safe. that is impossible! but if you discover only two houses are available, you know exactly where the agents must be — even if those houses could theoretically hold other people too.

a hidden pair works the same way: two numbers, two cells, no other options.

hidden pair vs. obvious pair

both techniques involve two cells and two numbers, but they look very different at first glance.

obvious pair

two cells have exactly the same two candidates

1
9
4
 2     8 
6
7
 2     8 
3
5

both cells show only [2, 8]

hidden pair

two cells have extra candidates, but only they can hold 2 and 8

1
9
4
 2  5  89
6
7
 23   78 
3
5

cells have [2, 8, 5, 9] and [2, 8, 3, 7] — but 2 & 8 are locked to these two

the difference: obvious pairs are easy to spot because the cells only have two candidates. hidden pairs require you to scan and find numbers that are restricted to just two cells — even if those cells contain other candidates.

the discovery process

to find hidden pairs, scan each row, column, and box for numbers that appear in only two cells. when two different numbers share the exact same two cells, you have found a hidden pair!

step-by-step scanning:

  1. pick a unit (row, column, or box)
  2. for each number 1-9, count how many cells could contain it
  3. if a number appears in only two cells, note those positions
  4. if another number shares those same two cells, you have a hidden pair!
  5. eliminate all other candidates from those two cells

summary

  • a hidden pair occurs when two numbers can only go in the same two cells
  • those cells may have additional candidates (that is what makes it "hidden")
  • scan by number to find which cells are the only options for each digit
  • when two numbers share the same two cells, eliminate other candidates from those cells
  • this often reveals an obvious pair that can trigger further eliminations
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