The family of giants you work for is throwing a fancy dinner party, and they all want to look their best. But there’s a problem – the elder giant’s favorite shirt is wrinkled! To fix it, you’ll need to power up… the Giant Iron.
你工作的巨人家庭 打算开一个别开 生面的晚会派对, 所以他们都希望凸显 自己最好的一面。 但是,有个问题—— 比较年长的巨人 最喜欢的衣服皱了! 为了解决它,你 需要启动…… 巨大的熨斗。
The iron needs two giant batteries to work. You just had 4 working ones and 4 dead ones in separate piles, but it looks like the baby giant mixed them all up. You need to get the iron working and press the giant shirt, fast – or you’ll end up being the main course tonight!
这个巨大的熨斗需要 两个巨大的电池运作。 你只有四个正常运作的电池, 还有四个耗损了的电池 在不同的电池堆里, 但是看来巨人宝宝把 它们给混在一起了。 你需要让熨斗运作,然后 烫巨人的衣服,而且要很快—— 不然的话,你就是今晚的主菜!
How can you test the batteries so that you’re guaranteed to get a working pair in 7 tries or less?
你能够如何测试电池, 以确保你能够在七个或以下的 尝试内就找到一对可用的电池?
Pause the video now if you want to figure it out for yourself Answer in 3 Answer in 2 Answer in 1
若你想自己想想方法, 请暂停影片。 答案在3秒后出现 答案在2秒后出现 答案在1秒后出现
You could, of course, take all eight batteries and begin testing the 28 possible combinations. You might get lucky within the first few tries. But if you don’t, moving the giant batteries that many times will take way too long. You can’t rely on luck – you need to assume the worst possibility and plan accordingly.
你当然可以拿全部八个电池, 然后开始试试二十八 个可能的组合。 你可能在初开始的 几个尝试就很幸运。 但是若不然,移动 大电池这么多次 会消耗太多时间。 你不能靠运气—— 你需要作最坏的打算, 然后做好策划。
However, you don’t actually need to test every possible combination. Remember – there are four good batteries in total, meaning that any pile of six you choose will have at least two good batteries in it. That doesn’t help you right away, since testing all six batteries could still take as many as 15 tries. But it does give you a clue to the solution – dividing the batteries into smaller subsets narrows down the possible results.
但是,你其实不需要 尝试所有的可能组合。 记得——总共有 四个好的电池。 也就是说在任何六个电池的组合里, 会有至少两个好的电池。 那没有直接帮助到你, 因为尝试所有六粒电池 还是需要十五次的尝试。 但是,它给了你 解决方案的提示—— 把电池分成小组缩小可能的结果。
So instead of six batteries, let’s take any three. This group has a total of three possible combinations. Since both batteries have to be working for the iron to power up, a single failure can’t tell you whether both batteries are dead, or just one. But if all three combinations fail, then you’ll know this group has either one good battery, or none at all. Now you can set those three aside and repeat the process for another three batteries. You might get a match, but if every combination fails again, you’ll know this set can have no more than one good battery. That would leave only two batteries untried. Since there are four good batteries in total and you’ve only accounted for two so far, both of these remaining ones must be good.
所以,与其六个电池, 让我们拿任何三个。 这个小组有三个组合。 因为要让熨斗运作需要 两个电池都正常运作, 其中一个失败并不会告诉你是两个 电池都不能用,还是只是其中一个。 但是若三个组合都失败, 你就能够知道这个小组里是有 一个好的电池,或一个也没有。 现在你可以把这 三个放在一边了 然后重复同样的过程 在在另外三个电池。 你有可能得到对的组合, 但是若每个组合都又失败, 那你就知道这个组合不可能 有超过一个好的电池。 那最后你剩下两个还未试过的电池。 因为总共有四个好的电池 而你只处理了两个, 这剩下的两个必然是好的。
Dividing the batteries into sets of 3, 3, and 2 is guaranteed to get a working result in 7 tries or less, no matter what order you test the piles in.
把电池分成三、三、二, 必然能够在七次尝试 找到可行的结果, 无论你是用什么次序尝试。
With no time to spare, the iron comes to life, and you manage to get the shirt flawlessly ironed. The pleased elder and his family show up to the party dressed to the nines … well, almost.
在没有剩余时间的情况下, 熨斗开始运作了, 而你也成功地把衣服 没有瑕疵地烫好了。 那个欢喜的年长巨人和他的 家人衣着隆重地参加了派对 ……嗯,差不多如此。