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.
一个吸血鬼猎人 能完成的最伟大的任务, 就是把阳光带进吸血鬼的巢穴里。 你已经偷偷地潜入了 吸血鬼的黑暗洞口, 把一面一面的镜子按角度架起来。 当外面的太阳升起到 一定角度的时候, 一束阳光会被镜子折射到洞内, 打到你准备好的聚光灯上, 然后就可以照亮 吸血鬼们睡觉的大堂。
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.
你把最后一面镜子架好, 然后偷偷潜入了大堂的一角。 聚光灯只能被安在墙上, 但几乎所有的墙附近 都有吸血鬼睡觉的棺材, 所以你不敢去把他们吵醒。 唯一可行的就是 大堂内的其它三个角落。
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.
这束阳光会从西南角 以45度方向进入, 然后会在大堂内光滑的四壁折射, 直到这束光打到 另外三个角中的其中一角。 但是,到底哪一个角落会被击中呢? 你知道这个大堂是一个 49米宽78米长的长方形。
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.
你估计可以这样慢慢找到答案: 把大堂按比例画在纸上, 然后追寻光的轨迹, 但是太阳马上就要升起了, 你没法浪费时间。 不过好在,还有另一种方法 可以解决这个难题, 这种方法非常简洁明了。
So in which corner should you place the diffuser to flood the vampire lair with sunlight?
那现在让咱们看看, 到底在哪个角落放聚光灯 才能成功杀死吸血鬼呢?
Pause the video if you want to figure it out for yourself.
如果你想自己思考答案, 可以现在暂停视频。
Answer in 2
离答案公布还有:2秒。
Answer in 1
1秒。
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.
想要解决这道题, 可以先看看小一点的房间, 然后你会发现一些有意思的规律。 有一个秘诀可以让你 迅速解决这道难题。
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.
让我们先把这个大堂 按比例画在图纸上, 把西南角的坐标定为(0,0) 这束阳光的轨迹射入的 坐标点都有一个共性: 两坐标要么都是偶数, 要么都是奇数。 即使这束光经过不同的墙壁 反射后也还是如此。 换种方法解释,就是说: 因为这束光是以45度角折射进入的, 所以它只会沿着每一个方格的对角线走, 横着移动1米等于在x轴上移一格, 把偶数变成奇数,或者相反。 竖着移动1米等于在y轴上移一格, 把偶数变成奇数,或者相反。 沿着对角线走就是横竖都移动, 所以,这束光经过的任何一点, 一定是两坐标全是偶数, 或者两坐标全是奇数。 这就是我们解决这道题的关键。 也就是说,我们找到了一个规律来区分 光会经过的点和不会经过的点。 如果一个点一个坐标是偶数,另一坐标是奇数 那么光就不会经过。 如此可以看出,这束光不会打到大堂的上两角 因为这两个角的横纵坐标奇偶不同。 也就是说,东南角是唯一 可以放聚光灯的地方。
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.
果然,当那束宝贵的阳光 打进大堂的时候, 它沿着四壁折射, 最后集中了东南角的聚光灯! 这时,吸血鬼们发现了有入侵者, 他们从棺材里爬出来, 但是被阳光化为灰烬。 这是一道“高风险”的问题, 恭喜你顺利过关!