"Unleashing Solar Fury: A Vampire Hunter's Daring Quest to Illuminate the Lair"

In the shadowy realm of vampire hunting, where legends and myths collide with reality, one challenge looms larger and more daring than all others – bringing the piercing sunlight into the heart of a vampire's dark and forbidding lair. As the intrepid vampire hunter, you descend stealthily into the depths of this cavern, armed with a singular purpose: to set the stage for an intricate play of angles and reflections that will bathe the vampire's resting chamber in sunlight. It is a race against time, with a sequence of mirrors and the sun's movement serving as the only allies on your side.

The plan is simple yet intricate: as the sun reaches the perfect angle in the sky, a beam of concentrated light will ricochet from mirror to mirror, ultimately striking your diffuser. The diffuser, crucial in this plot, must be securely mounted on a wall. However, a formidable challenge presents itself. The chamber's walls are crowded with ancient coffins, each harboring a dormant vampire – creatures of immense power and potentially unforgiving malevolence. Disturbing these slumbering behemoths is unthinkable. So, your options are confined to the three remaining corners of the room. The tension rises as the sun nears its zenith. Time is of the essence, and there's no room for cumbersome calculations or the luxury of sketching scale models.

Yet, you possess a secret weapon – an elegant, straightforward solution that lies just beyond the apparent complexity of the task. In which corner should you position the diffuser to release a torrent of sunlight and vanquish the vampires? Take a moment to ponder this conundrum if you wish.

The crux of this enigma revolves around seeing the chamber as a rectangular grid, where the southwest corner serves as the reference point (0,0). Astonishingly, there emerges a distinct pattern in the path of the light: it passes through grid points with coordinates that are consistently either both even or both odd, even after multiple deflections from the walls. In other words, the sunlight's trajectory intersects with the diagonal of a unit square, and it holds true even in the case of multiple bounces.

Imagine it this way: Moving horizontally by one meter transitions the x-coordinate from even to odd or vice versa. Similarly, progressing vertically by one meter triggers the same transformation in the y-coordinate. However, as the light traverses diagonally, as it does in this situation, it essentially accomplishes both transformations simultaneously. As a result, the x and y coordinates of any point the light crosses must be either both even or both odd.

This apparently straightforward observation contains the pivotal key to unlocking the riddle. Significantly, it provides a means to pinpoint the precise points the light will never pass through. Should one coordinate be even and the other odd, the light will consistently bypass these points, ensuring they remain untouched. In light of this revelation, it becomes evident that the top two corners of the room, each with one even and one odd coordinate, are perpetually immune to the sunlight's touch.

With this newfound understanding, the Southeast corner emerges as the sole contender for the placement of the diffuser. As the sunlight filters into the chamber, it weaves an intricate dance between the walls and finally strikes the Southeast corner, casting a brilliant, radiant blaze upon the lair.

As the first rays of light flood the chamber, the vampires, sensing the intrusion, burst from their coffins and are promptly reduced to mere wisps of dust. It was a high-stakes test, a duel of wits and cunning, and you, the fearless vampire hunter, emerged triumphant. Your ingenious solution has not only unveiled the secrets of this vampire's lair but has also banished these creatures of the night with the power of sunlight, forever keeping darkness at bay.