Naked Triplet Walkthrough
A Naked Triplet is three cells in a unit whose candidates are drawn from the same three digits. Those digits are confined to those three cells and can be cleared from the rest of the unit.
There is a Naked Triplet in Block 2. Applying the Naked Triplet eliminates 1 candidate (struck out in red below; any solved cells shown in green).
Reading this board
The pattern on this puzzle involves box 2. Work from the before-image above: find the naked triplet for yourself before scrolling to the after-image, since the point of a worked example is the search, not the answer. This move removes a single candidate. That is typical and not a disappointment — one elimination is often the exact one that turns a neighbouring cell into a single.
Why the deduction is valid
Three cells in a unit whose candidates are drawn from the same three digits must consume all three of those digits between them. The subtlety is that the individual cells need not show all three — {1,4}, {4,9} and {1,9} is a perfectly good Naked Triplet, because those three cells still have nowhere to go outside the set {1,4,9}. Three cells, three digits, no room for anything else: the digits are locked in, and clear out of the rest of the unit.
How to spot a Naked Triplet on your own board
- Look for clusters of cells in one unit whose candidates all come from a small pool. Take the union of three cells’ candidates; if the union has exactly three members, you have a triplet.
- The partial forms are the ones people miss. Two-candidate cells that interlock in a ring, like {3,6}, {6,8}, {3,8}, are far more common than three cells each showing all three digits.
- Units already holding five or six placed digits are the best hunting ground, since few candidates remain to form the pool.
Common mistakes
- Counting a union of four digits as a triplet. Three cells covering four candidates locks nothing.
- Overlooking that the triplet may span a box as well as a line, in which case the eliminations apply in both units.
What to do next
Triplets often unlock the unit dramatically, since removing three digits from the remaining cells can leave several of them with one candidate each. Sweep the whole unit for singles before moving on.