Video transcript
A clue of two, one means two separate groups. The first number is a pair of touching filled squares. The second number is one filled square later in the line, and the order cannot change.
The groups need at least one empty square between them. If the pair touched the single square, they would form one run of three, which would be a clue of three—not two, one.
A line may have the correct group sizes but the wrong order, or it may merge everything into one group. A valid arrangement must preserve the sizes, order, and required gap.
Even then, the clue does not always determine every exact position. In five cells there are three legal placements. Compare them and cell two is filled every time, so it is guaranteed even though the rest of the line remains unresolved.
Remember four checks: each number is a group size, groups stay in order, separate groups need a gap, and cells shared by every legal placement are safe to fill.