Expert technique

Hidden Triples, Explained

When three colors can only go in the same three cells, those cells belong to them, no matter how much else is written there.

Read the block

BEFORE

Eight of the nine cells in this block are open, which is about as crowded as notes ever get. Every technique so far finds nothing here: no cell shows a single color, no color has a single place, no cells pair, no cells triple, and no two colors share the same two places. What is left is to count places three colors at a time.

Find three colors sharing the same three cells

Red appears in two cells of the top row. Light Purple appears in all three. Orange appears in two. Between them, those three colors never appear anywhere but that row, and the row is exactly three cells long. Three colors, three cells, so the row belongs to them.

Clear everything else out of them

The three colors do not have to be spread evenly. The top left cell shows all three, the other two show two each, and that changes nothing. Between them the three colors have nowhere else to go, and there are exactly three cells to hold them, so no fourth color can fit. Turquoise and Dark Purple come off the row.

Read what that leaves

AFTER

Dark Purple could go in two cells of this block, and one of them was in the row that now belongs to the triple. That leaves one place, in the bottom right, so Dark Purple must go there. The triple is no closer to being solved, and once again it did not need to be.

Cells being readKey cellColor tints match the color being followed

Key Insight

This is the last of the four matching-group techniques, and it is the same idea every time: a group of cells and a group of colors that are the same size and belong to each other. You find obvious groups by reading cells, and hidden groups by counting where colors can go. Hidden Triples is worth the effort exactly when a block looks hopeless, because the more crowded the cells are, the better the pattern hides. Clearing three cells at once usually leaves some color with only one place left.

If you’re stuck on a puzzle, see what to try next, in order.