The greatest challenge a vampire hunter  can take on is to bring sunlight  into a vampire's lair. You’ve stealthily descended into the  darkness of a vampire cave, setting a sequence of mirrors as you go. When the sun reaches  the right angle in the sky, a focused beam of light will ricochet  along the mirrors, strike your diffuser, and illuminate the great chamber  where the vampires sleep. You set the final mirror and sneak through an opening  in the corner of the great chamber. The diffuser must be wall-mounted, but the walls are crowded with coffins, which you don’t dare disturb. The only open spots are in the other  three corners of the room. The light will enter through the southwest corner at a 45 degree angle and bounce off the perfectly smooth  metallic walls until it hits one of the  other three corners. But which corner will it hit? You know the room is a rectangle 49 meters wide and 78 meters long. You could probably find the answer by drawing a scale model of the room  and tracing the path of the light, but the sun will be in its  place in just minutes, and you’ve got no time to spare. Fortunately, there’s a different way to solve this puzzle that’s both simple and elegant. So in which corner should  you place the diffuser to flood the vampire lair with sunlight? Pause the video if you want to figure it out for yourself. Answer in 2 Answer in 1 You could tackle this problem  by examining smaller rooms, and you’d find a lot  of interesting patterns. But there’s one insight that can unravel  this riddle in almost no time at all. Let’s draw the chamber  on a coordinate grid, with the Southwest corner  at the point (0,0). The light passes through grid points with coordinates that are either  both even or both odd. This is true even after it bounces off  one or more walls. Another way of thinking about it is this: since the light travels at a  45 degree angle, it always crosses the diagonal  of a unit square. Traveling 1 meter horizontally  changes the x coordinate from even to odd or vice versa. Traveling 1 meter vertically  changes the y coordinate from even to odd or vice versa. Traveling diagonally – as the light  does here – does both at once, so the x and y coordinates of any points  the light passes through must be both even, or both odd. This observation is more  powerful than it seems. In particular, it means that we have a  way to identify the kinds of points the light won’t ever go through If one of the coordinates is even  and the other is odd, the light will miss them. That means it’ll miss the top  two corners of the room, since those points have one even  and one odd coordinate. The Southeast corner is the  only option for the diffuser. And indeed, when that precious  beam of sunlight enters the hall, it bounces between the walls and strikes the Southeast corner, spot on. The vampires, sensing the intrusion, burst from their coffins  and turn to dust in the light. It was a “high stakes” test, and you passed with flying colors.