You’re on the trail of a werewolf that’s been terrorizing your town. After months of detective work, you’ve narrowed your suspects to one of five people: the mayor, the tailor, the baker, the grocer, or the carpenter.
你正在追踪着一只 对你的小镇虎视眈眈的狼人。 经过数个月的侦查, 你锁定了五个嫌疑人: 镇长、 裁缝、 面包师、 杂货商 或木匠。
You’ve invited them to dinner with a simple plan: you’ll slip a square of a rare werewolf antidote into each of their dinners. Unfortunately, your pet goat just ate four of the squares, and you only have one left.
你邀请他们共进晚餐,计划很简单: 你将会在每个人的晚餐中 悄悄放入一片稀有的正方形狼人解药。 不幸的是,你的宠物山羊 刚刚吃掉了四片解药, 所以你只剩下了一片。
Luckily, the remaining square is 50 grams, and the minimum effective dose is 10 grams. If you can precisely divide the square into fifths you’ll have just enough antidote for everyone.
幸运的是,剩下的这一片重 50 克, 而最小有效剂量是 10 克。 如果你能准确地 把这个正方形一分为五, 那每个人都能得到一份解药。
You’ll have to use a laser-cutting tool to cut up the square; every other means available to you isn’t precise enough. There are 8 points that can act as starting or ending points for each cut. To use the device, you’ll have to input pairs of points that tell the laser where to begin and end each cut, and then the laser executes all the cuts simultaneously.
你必须使用一台激光切割机, 其它所有方式都不够精确。 有八个点可以充当 每次切割的起点或终点。 每一道切割,你都必须输入两个点 作为切割的起点和终点。 仪器会一次性执行 你设置好的所有切割。
It’s okay to cut the square into as many pieces as you want, as long as you can group them into 10 gram portions. But you can’t fold the square or alter it otherwise, and you only get one shot at using the laser cutter. The full moon is rising, and in a moment someone will transform and tear you all apart unless you can cure them first.
无论切成多少块都没有关系, 只要最后能把药片 凑成10克的份量即可。 但你不能把正方形折起来, 或者用其它方式改变它 而且你只有一次使用激光切割机的机会。 满月正在升起, 再过一会就会有人变身狼人 把你们撕成碎片, 除非你预先治好那个人。
How can you divide the antidote into perfect fifths, cure the secret werewolf, and save everyone?
你要如何将解药完美地平分成五份, 治好藏在五人之中的狼人, 拯救大家呢?
Pause the video now if you want to figure it out for yourself.
如果想要自己解开谜题, 请在此画面暂停。
Answer in 3
答案揭晓:3
Answer in 2
答案揭晓:2
Answer in 1
答案揭晓:1
When it comes to puzzles that involve cutting and rearranging, it’s often helpful to actually take a piece of paper and try cutting it up to see what you can get. If we cut BF and DH we’d get fourths, but we need fifths. Maybe there’s a way to shave a bit off of a quarter to get exactly one fifth. Cutting BE looks good at first, but that last cut takes a off a quarter of a quarter, leaving us with a portion of 3/16: just smaller than a fifth, and not enough to cure a werewolf.
对于跟分割和重组有关的谜题, 拿起一张纸尝试实际切割 通常很有帮助。 沿着 BF 和 DH 切割可将其一分为四, 但我们需要五份。 或许有办法可以往四分之一上 再切一点,得到五分之一。 BE 乍一看是个好选择, 但这会切掉四分之一的四分之一, 剩下十六分之三, 比五分之一略小了一点, 不足以治愈狼人。
What if we started with BE instead? That would also give us a quarter. And is there a way to shave just a bit more off? Both DG and CH look promising. If we make one more cut, from A to F, we may start to notice something.
那要是从 BE 开始切割呢? 这也会使我们得到四分之一。 还能再切掉一点吗? DG 和 CH 看起来都像是不错的选择。 如果我们再沿着 AF 切一道, 我们就会发现:
With these four cuts—from B to E, D to G, F to A, and H to C—we’ve got four triangles and a square in the middle. But the pieces that make each triangle can also be rearranged to make a square identical to the middle one. This means that we’ve split the antidote into perfect fifths!
若沿着这四条线切割—— B 至 E、D 至 G、F 至 A、 H 至 C——我们就会得到四个三角形 和中间的一个正方形。 但组成每个三角形的切片 都能被重新拼成一个 跟中间那个一模一样的正方形, 由此,我们成功地将解药平分成了五份!
What’s interesting about this sort of problem is that while it’s possible to solve it by starting from the geometry, it’s actually easier to start experimenting and see where that gets you. That wouldn’t be as viable if the square had, say, 24 cut points, but with just 8 there are only so many reasonable options.
关于这类问题,有趣的是 尽管几何学计算也能帮你找出答案, 但直接动手尝试反而比较容易。 虽然如果正方形上有 24 个点之类的话 反复试验自然不太现实, 但只有 8 个点的话 只有那么多选择供你尝试。
You secretly dose each of the townspeople as the full moon emerges in the sky. And just as you do, a terrible transformation begins. Then, just as suddenly, it reverses. Your measurements were perfect, and the people and animals of the town can rest a little easier.
随着满月在夜空中出现, 你将解药偷偷放进每个人的饭菜里。 你刚刚搞定一切, 可怕的变身就猛地开始, 紧接着又同样迅速地被扭转了。 你的剂量完美, 小镇里的居民和动物又得以安心了。