Can you solve the giant iron riddle? - Alex Gendler

2,572,780 views ・ 2018-11-27

TED-Ed


请双击下面的英文字幕来播放视频。

翻译人员: Meng Chew Keane Leow 校对人员: Tianji (Homer) Li
00:07
The family of giants you work for
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你工作的巨人家庭
00:10
is throwing a fancy dinner party,
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打算开一个别开 生面的晚会派对,
00:12
and they all want to look their best.
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所以他们都希望凸显 自己最好的一面。
00:14
But there’s a problem –
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但是,有个问题——
00:16
the elder giant’s favorite shirt is wrinkled!
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比较年长的巨人 最喜欢的衣服皱了!
00:19
To fix it, you’ll need to power up…
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为了解决它,你 需要启动……
00:21
the Giant Iron.
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巨大的熨斗。
00:23
The iron needs two giant batteries to work.
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这个巨大的熨斗需要 两个巨大的电池运作。
00:26
You just had 4 working ones
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你只有四个正常运作的电池,
00:28
and 4 dead ones in separate piles,
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还有四个耗损了的电池 在不同的电池堆里,
00:31
but it looks like the baby giant mixed them all up.
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但是看来巨人宝宝把 它们给混在一起了。
00:34
You need to get the iron working and press the giant shirt, fast –
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你需要让熨斗运作,然后 烫巨人的衣服,而且要很快——
00:38
or you’ll end up being the main course tonight!
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不然的话,你就是今晚的主菜!
00:41
How can you test the batteries
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你能够如何测试电池,
00:43
so that you’re guaranteed to get a working pair in 7 tries or less?
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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?
00:48
Pause the video now if you want to figure it out for yourself
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若你想自己想想方法, 请暂停影片。
00:52
Answer in 3
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答案在3秒后出现
00:53
Answer in 2
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答案在2秒后出现
00:54
Answer in 1
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答案在1秒后出现
00:55
You could, of course, take all eight batteries
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你当然可以拿全部八个电池,
00:57
and begin testing the 28 possible combinations.
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然后开始试试二十八 个可能的组合。
01:01
You might get lucky within the first few tries.
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你可能在初开始的 几个尝试就很幸运。
01:03
But if you don’t, moving the giant batteries that many times
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但是若不然,移动 大电池这么多次
01:07
will take way too long.
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会消耗太多时间。
01:08
You can’t rely on luck –
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你不能靠运气——
01:10
you need to assume the worst possibility and plan accordingly.
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你需要作最坏的打算, 然后做好策划。
01:14
However, you don’t actually need to test every possible combination.
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但是,你其实不需要 尝试所有的可能组合。
01:19
Remember – there are four good batteries in total,
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记得——总共有 四个好的电池。
01:23
meaning that any pile of six you choose
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也就是说在任何六个电池的组合里,
01:26
will have at least two good batteries in it.
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会有至少两个好的电池。
01:28
That doesn’t help you right away,
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那没有直接帮助到你,
01:30
since testing all six batteries could still take as many as 15 tries.
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因为尝试所有六粒电池 还是需要十五次的尝试。
01:35
But it does give you a clue to the solution –
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但是,它给了你 解决方案的提示——
01:38
dividing the batteries into smaller subsets narrows down the possible results.
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把电池分成小组缩小可能的结果。
01:43
So instead of six batteries,
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所以,与其六个电池,
01:45
let’s take any three.
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让我们拿任何三个。
01:47
This group has a total of three possible combinations.
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这个小组有三个组合。
01:51
Since both batteries have to be working for the iron to power up,
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因为要让熨斗运作需要 两个电池都正常运作,
01:54
a single failure can’t tell you whether both batteries are dead, or just one.
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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。
01:59
But if all three combinations fail,
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但是若三个组合都失败,
02:02
then you’ll know this group has either one good battery, or none at all.
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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。
02:07
Now you can set those three aside
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现在你可以把这 三个放在一边了
02:09
and repeat the process for another three batteries.
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然后重复同样的过程 在在另外三个电池。
02:12
You might get a match, but if every combination fails again,
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你有可能得到对的组合, 但是若每个组合都又失败,
02:16
you’ll know this set can have no more than one good battery.
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那你就知道这个组合不可能 有超过一个好的电池。
02:20
That would leave only two batteries untried.
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那最后你剩下两个还未试过的电池。
02:23
Since there are four good batteries in total
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因为总共有四个好的电池
02:25
and you’ve only accounted for two so far,
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而你只处理了两个,
02:28
both of these remaining ones must be good.
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这剩下的两个必然是好的。
02:31
Dividing the batteries into sets of 3, 3, and 2
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把电池分成三、三、二,
02:34
is guaranteed to get a working result in 7 tries or less,
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必然能够在七次尝试 找到可行的结果,
02:38
no matter what order you test the piles in.
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无论你是用什么次序尝试。
02:41
With no time to spare, the iron comes to life,
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在没有剩余时间的情况下, 熨斗开始运作了,
02:44
and you manage to get the shirt flawlessly ironed.
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而你也成功地把衣服 没有瑕疵地烫好了。
02:47
The pleased elder and his family show up to the party dressed to the nines
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那个欢喜的年长巨人和他的 家人衣着隆重地参加了派对
02:52
… well, almost.
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……嗯,差不多如此。
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