If you ever look at pictures of clocks and watches in advertising they are set to roughly 10:10 which is meant to be the most attractive (smiling!) position for the hands . They are actually set to 10:09.14 if the hands are truly symmetrical. CC BY 2.0 image by Shinji I wanted to know what all the possible symmetrical watch faces are and so I wrote some code using Processing. Here's the output (there's one watch face missing, 00:00 or 12:00, because it's very boring): The key to writing this is to figure out the relationship between the hour and minute hands when the watch face is symmetrical. In an hour the minute hand moves through 360° and the hour hand moves through 30° (12 hours are shown on the watch face and 360/12 = 30). The core loop inside the program is this: for (int h = 0; h <= 12; h++) { float m = (360-30*float(h))*2/13; int s = round(60*(m-floor(m))); int col = h%6; int row = floor(h/6); draw_clock((r+f)*(2*col+1), (r+f)*(row*2+1),