Test a Bubble: Trial and Error Without Blind Guessing

No cell on this board shows a single color, no color has just one place left, and no pair, triple, or line pattern places anything. That is exactly when this technique works best. Eight cells here show just two colors, and the shaded one holds Red and Light Purple.

Put a Red in that cell, just to see. This is not a guess, because we are not going to keep it. We are going to follow what it forces and watch whether the board breaks, and either answer is useful.

Placing the test Red removes Red from every cell it can see, and one of those is in the same block, just below and to the right. That cell only ever held Red and Light Purple, so with Red gone it has to be Light Purple. Nothing was chosen there. It was forced.

Now the same thing happens along the row. The forced Light Purple removes Light Purple from the cells it can see, including one further along its own row that also held only Red and Light Purple. So that one becomes Red. Two moves in, and we have not made a single choice.

Look at the second row from the top, shaded dark. Only two of its cells could ever have held a Red, and the two lighter columns show what happened to them: the test bubble used up one, and the Red it forced used up the other. Every row must hold a Red somewhere. This one now has nowhere to put it, which cannot happen on a real board.

Red led straight to an impossible board, so Red was never an option in that cell. Take the three test bubbles back off and place Light Purple instead. Nothing here was guessed. It was proved, and a proof holds no matter how long the chain took to find it.