English: Graphical solution to the puzzle of what times hour and minute hands of a 12-hour clock are aligned by CMG Lee. T denotes time in hours; P, hands' positions; and θ, hands' angles in degrees. The red (thick solid) line denotes the hour hand; the blue (thin solid) lines denote the minute hand. Their intersections (red squares) are when they align. Additionally, orange circles (dash-dot line) are when hands are in opposition, and pink triangles (dashed line) are when they are perpendicular. In the SVG file, hover over the graph to show the positions of the hands on a clock face.