zedoku

hidden triples

level 4 - hard

three numbers can only go in three specific cells (even if those cells have other candidates).

what it means

a hidden triple occurs when three numbers are restricted to exactly three cells within a unit (row, column, or box). even though those cells may contain other candidates, the three numbers can only appear in those three cells. this means we can eliminate all other candidates from those three cells!

🕵️ the secret agents in houses analogy

imagine three secret agents (agent 2, agent 8, and agent 9) who need to hide in a neighborhood. there are several houses available, but due to security protocols:

  • agent 2 can only hide in houses a, b, or c
  • agent 8 can only hide in houses a, b, or c
  • agent 9 can only hide in houses a, b, or c

even though houses a, b, and c might have space for other agents too, agents 2, 8, and 9 must occupy these three houses. any other "candidate" agents hoping to hide in houses a, b, or c must leave — those houses are reserved for agents 2, 8, and 9!

example 1: before - three cells with many candidates

look at the center cell in this box. it has candidates 2, 5, 8, and 9. at first glance, there seems to be no pattern.

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center cell has candidates: 2, 5, 8, 9

but let's look deeper. which cells in this box can contain the numbers 2, 8, and 9?

example 2: analysis - finding the restriction

let's check where each number can go in this box:

  • number 2: only appears in the center cell
  • number 8: only appears in the center cell
  • number 9: only appears in the center cell

wait — actually this is a hidden single! let's look at a more complex example where we truly have three cells sharing three numbers.

in a proper hidden triple scenario, imagine three cells each containing candidates like:

  • cell a: candidates [2, 5, 7, 8, 9]
  • cell b: candidates [2, 5, 6, 8, 9]
  • cell c: candidates [2, 5, 6, 7, 9]

if we discover that numbers 2, 8, and 9 only appear in these three cells, we have a hidden triple! the other candidates (5, 6, 7) can be eliminated.

example 3: row-based hidden triple

here's a clearer example in a row. look at the three empty cells:

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three cells all contain candidates 3 and 7

in this case, numbers 3 and 7 form a hidden pair(a simpler version of the same concept). all empty cells can only be 3 or 7, and those numbers only appear in these cells.

obvious triples vs hidden triples

obvious triples

three cells contain onlythree shared candidates total.

example:
cell a: [2, 5, 8]
cell b: [2, 5, 8]
cell c: [2, 5, 9]

the candidates are "obvious" — visible immediately in the cells.

hidden triples

three cells have morecandidates, but three numbers are restricted to only those cells.

example:
cell a: [2, 5, 6, 8, 9]
cell b: [2, 5, 6, 8, 9]
cell c: [2, 5, 6, 7, 9]
→ but 2, 8, 9 only in these cells!

the pattern is "hidden" — requires checking where numbers can go.

the key difference: obvious triples look at what candidates cells have, while hidden triples look at where numbers can be placed.

step-by-step walkthrough

step 1: find three numbers that appear in limited cells

scan a row, column, or box. look for three numbers that don't have many placement options. for example, check if numbers 2, 6, and 7 each appear as candidates in only 2-3 cells.

step 2: check if they're confined to three cells

verify that all three numbers are restricted to exactly the same three cells. if number 2 can go in cells a, b, c; number 6 can go in a, b, c; and number 7 can go in a, b, c — you've found a hidden triple!

step 3: remove other candidates from those cells

since those three cells must contain those three numbers (in some order), you can eliminate all other candidates from those cells. this often reveals singles or other patterns!

why it works

the logic is simple but powerful:

  • if three numbers can only go in three specific cells
  • then those three cells must contain those three numbers
  • therefore, those cells cannot contain any other numbers
  • eliminating other candidates often solves other cells!

💡 advanced note: take your time

hidden triples are considered a level 4 technique for a reason — they're significantly harder to spot than obvious patterns. it's completely okayif this technique takes time to master!

many experienced sudoku solvers skip looking for hidden triples and instead look for easier patterns first. only when a puzzle is truly stuck do they search for these advanced patterns.

keep practicing — with experience, you'll start spotting these patterns naturally!

quick summary

hidden triple: three numbers that can only appear in three specific cells within a unit. even though those cells may have other candidates, the triple numbers are confined to those cells, allowing you to eliminate all other candidates from them.

obvious triplesnext: x-wing →