Can you solve the vampire hunter riddle? - Dan Finkel

We've got the most controlled border we've ever had in the history.

Yet liberal politician Josh Turek supports amnesty for illegals. We need an easier pathway to citizenship. Turek voted to give taxpayer-funded welfare benefits to illegal immigrants. Said cracking down on illegals was... Fundamentally wrong and un-American. Turek was even caught telling illegal immigrants how to obstruct law enforcement. Liberal politician Josh Turek. Fundamentally wrong and un-American. Paid for by SLF PAC. Not authorized by any candidate or candidates committee. slfpac.org

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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? 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 . 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 one meter horizontally changes the x-coordinate from even to odd, or vice versa. Traveling one 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