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AlexRosenthal_SubmarineRiddle_2021E-_你能够解开离群潜水艇的谜题吗?难度:大师级别_
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Smuggling yourself aboard the rogue submarine was the easy part. |
偷溜上离群的潜水艇是最容易的一步。 |
Hacking into the nuclear missile launch override— a little harder. |
黑进核导弹发射超控就有些难度了。 |
But now you’ve got a problem: you don’t have the override code. |
但是有个问题:你不知道 用来阻止发射的密码。 |
You know you need the same two numbers that the agents of chaos just used to authorize the launch. |
你知道需要输入 混乱之敌特刚用来 开启发射的两个数字。 |
Smuggling:n.走私(罪);v.走私;私运;偷运;(smuggle的现在分词) aboard:adv.在飞机上;[船]在船上;在火车上;prep.在…上; rogue:n.流氓; v.游手好闲; adj.(野兽)凶猛的; submarine:n.潜艇;adj.水下的;海底的v.用潜艇攻击;驾驶潜艇; Hacking:v.黑客行为;砍;劈;猛踢;(hack的现在分词) nuclear:adj.原子能的;[细胞]细胞核的;中心的;原子核的; missile:n.导弹;发射物;投掷物; launch:v.发射(导弹,火箭等); n.发射; override:v.凌驾;(以权力)否决;比…更重要;超驰控制; agents:n.代理人,经纪人;原动力;(agent的复数) chaos:n.混沌,混乱; authorize:vt.批准,认可;授权给;委托代替;
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But one wrong answer will lock you out. |
可是答错一次,超控就会上锁。 |
From your hiding spot, you’ve been able to learn the following: |
你从隐藏的地方获得了以下的信息: |
The big boss didn’t trust any minion with the full information to launch nuclear missiles on their own. |
老大不够信任他的走狗们, 所以没把用来开启发射的全部信息 交给任何一个走狗。 |
So he gave one launch code to Minion A, the other to minion B, and forbade them to share the numbers with each other. |
于是他把开启密码的其中一个 交给走狗A,另外的交给走狗B, 并且禁止他们两互相分享密码。 |
When the order came, each entered their own number and activated the countdown . |
老大命令下来后, 他们各自输入了自己的密码, 启动了倒计时。 |
minion:n.奴才;宠臣;adj.娇美的,美雅的; missiles:n.导弹;发射物;投掷物;(missile的复数) forbade:v.禁止(forbid的过去式); activated:v.使活动;激活;使活化;(activate的过去式和过去分词) countdown:n.倒数计秒;
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That was 50 minutes ago, and there's only 10 minutes left before the missiles launch. |
那已经是50分钟前的事了。 距离导弹发射只剩下10分钟。 |
Suddenly, the boss says, “Funny story— your launch codes were actually related. |
老大突然道,“跟你们说件好笑的事情。 你们的开启密码其实是相关的。” |
I chose a set of distinct positive integers with at least two elements , each less than 7, and told their sum to you, A, and their product to you, B.” |
我选择了一组至少有两个元素的 不同正整数,各自小于 7, 把总和告诉了A,把乘积告诉了B。 |
After a moment of awkward silence, A says to B, |
尴尬的一瞬间后,A对B说: |
B thinks this over, then responds , “I know your number, and now I know you know my number too.” |
B想了想,回答道: “我知道你的数字是多少, 现在也知道你也知道我的数字。” |
What numbers do you enter to override the launch? |
输入什么数字才能阻止发射? |
distinct:adj.明显的;独特的;清楚的;有区别的; positive:adj.积极的;[数]正的,[医][化学]阳性的;确定的;n.正数;[摄]正片; integers:n.[数]整数(integer的复数); elements:n.要素;基本部分;少量;一群;(element的复数) awkward:adj.尴尬的;笨拙的;棘手的;不合适的; responds:v.(口头或书面)回答,回应;作出反应;响应;(respond的第三人称单数)
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Pause now to figure it out for yourself. Answer in 3 |
想自己解答就请暂停视频。 3秒后公布答案 |
Answer in 2 |
2秒后公布答案 |
Answer in 1 |
1秒后公布答案 |
Ignorance-based puzzles like this are notoriously difficult to work through. |
像这样一个建立在无知的基础的谜题 是出了名的难解。 |
The trick is to put yourself in the heads of both characters and narrow down the possibilities based on what they know or don’t know. |
解题的窍门是通过两人的角度想, 然后根据他们知道和不知道的事 缩小可能性的范围。 |
So let's start with A's first statement . |
先从A说的第一句话开始吧。 |
puzzles:智力游戏;谜题(puzzle的第三人称单数和复数) notoriously:adv.众所周知地;声名狼藉地;恶名昭彰地; narrow down:缩小;限制;减少;变窄; statement:n.声明;陈述,叙述;报表,清单;
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It means that B could conceivably have something with the potential to reveal A’s number, but isn’t guaranteed to. |
那代表B可能知道一件 有可能能透漏A的数字是多少的事, |
That doesn’t sound very definitive , but it can lead us to a major insight . |
这听起来并不能确定, 却能使我们达到极重要的见解。 |
The only scenarios where B could know A’s number are when there’s exactly one valid way to factor B’s number. |
仅当B的数字只有一种 因数分解方式的时候 B才会知道A的数字的大小。 |
conceivably:adv.令人信服地;可相信地;想得到地; potential:n.潜能;可能性;[电]电势;adj.潜在的;可能的;势的; reveal:v.显示;透露;揭露;泄露;n.揭露;暴露;门侧,窗侧; guaranteed:adj.必然的; v.保证; definitive:n.限定词;adj.决定性的;最后的;限定的; insight:n.洞察力;洞悉; scenarios:n.情节;脚本;情景介绍(scenario的复数); valid:adj.有效的;有根据的;合法的;正当的; factor:n.因素;要素;[物]因数;代理人;v.做代理商;v.把…作为因素计入;
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Try factoring a few and you’ll find the pattern— |
你通过尝试整除几个数就会发现规律。 |
It could be prime— where the product must be of 1 and itself— or it could be the product of 1 and the square of a prime , such as 4. |
可能会是素数——也就是说, 它的因式必须是一和那个数字。 或者可能是一个有一和一个素数的二次方的因式,如四,的数字。 |
In both cases, there is exactly one sum. |
在这两种情况下,正好有一个和数。 |
factoring:n.[数]因子分解,[数]因式分解; v.把…因素包括进去(factor的现在分词); prime:adj.主要的; v.极好地; n.初期; v.使准备好;
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For a number like 8, factoring it into 2 and 4, or 1, 2, and 4, creates too many options . |
把一个像八一样的数字整除成二和四或一,二,和四的话, 就有太多可能性了。 |
Because the boss’s numbers must be less than 7, |
因为老大的数字都小于七, |
A’s list of B’s possibilities only has these 4 numbers. |
A能列为有可能是B的数字 只包括这四个数字。 |
Here’s where we can conclude a major clue . |
我们从此能判断出一个重要的线索。 |
To think B could have these numbers, A’s number must be a sum of their factors— so 3, 4, 5, or 6. |
A的数字必定是B数字的因式的和, B才能是这些数字之一。 也就是说是三,四,五,或六。[02:53] |
options:n.选择; v.得到或获准进行选择; (option的三单形式) conclude:v.断定:得出结论:终止:达成:缔结(协定) clue:n.提示;迹象;(纵横填字谜、游戏或问题的)提示词语;v.提示;为…提供线索;
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We can eliminate 3 and 4, because if the sum was either, the product could only be 2 or 3, in which case A would know that B already knows A’s number, contradicting A’s statement. |
可以排除三和四,因为和数 如果是其中的一个数的话, 那乘积就只能是二或三。 在那种情况下,A就已经知道 B知道A的数字了, 和A说的话恰恰相反。 |
5 and 6, however, are in play, because they can become sums in multiple ways. |
但是五和六都有可能, 因为这两个数字可以 以许多方式成为和。 |
The need to consider this is one of the most difficult parts of this puzzle. |
考虑这个的需要就是 这个谜题最难的部分之一。 |
eliminate:v.消除;排除; contradicting:n.矛盾;v.矛盾(contradict的ing形式);反驳;顶触; sums:n.算术题;总数;全部;v.归纳;总计;(sum的第三人称单数和复数) multiple:adj.数量多的;多种多样的;n.倍数;
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The crucial thing to remember is that there’s no guarantee those are just the possibilities from A’s perspective that would allow B to deduce A’s number. |
要记得的关键就是B的数字 这些只是A觉得有可能的数字, B也就能借此推断出A的数字是多少。 |
That ambiguity forces us to go through unintuitive multi-step processes like: consider a product, see what sums can result from its factors , then break those apart and see what products can result. |
这种模糊性迫使我们通过不直观、 多步骤的过程来考虑, 如: 考量一个乘积,看看乘积的因式 加起来是什么和数, 然后把那些和数分解成因式, 再找出因式的乘积。 |
crucial:adj.重要的;决定性的;定局的;决断的; perspective:n.观点;远景;透视图;adj.透视的; deduce:v.推论;推断;演绎; ambiguity:n.含糊;不明确;暧昧;模棱两可的话; multi-step:多步的; processes:n.过程; v.处理(process的第三人称单数形式); factors:n.因素(factor的复数); v.做代理商;
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We’ll soon have to do something similar going from sums to products and back to sums. |
我们马上就要做一件相似的事, 从和找到乘积,再回到和。 |
But now we know— when A made his first statement, he must have been holding either 5 or 6. |
但我们现在知道A说出第一句话时, 他的数字一定是五或六。 |
B has access to the same information we do, so he knows this too. |
B知道的信息和我们一样, 所以这他也知道。 |
Let’s review what’s in each brain at this point: everyone knows a lot about the sum, but only B knows the product. |
我们回顾一下大家现在都知道些什么: 大家都知道很多关系和数的信息, 但只有B知道乘积是多少。 |
Now let’s look at the first part of B’s statement. |
现在看看B说的话的第一部分。 |
What if A’s number was 5? |
A的数字要是是五呢? |
in which case B would have either 4 or 6. |
在这种情况下, B的数字不是四就是六。 |
4 would tell B what A had, like he said, because there’s only one option to make the product: 4 times 1. |
如果是四的话,B就知道 A的数字是什么了, 因为那样只有一种乘法,四乘以一。 |
What if:如果…怎么办?
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6, on the other hand , could be broken down three ways, which sum like so. |
六反而能以三种方法分解, 因式的和数如以上。 |
7 isn’t on B’s list of possible sums, but 5 and 6 both are. |
B觉得有可能的和数不包括七, 但包括五和六。 |
Meaning that B wouldn’t know whether A’s number was 5 or 6, and we can eliminate this option because it contradicts his statement. |
那代表B就不知道 A的数字是五还是六了, 所以我们就能排除这个可能性, 因为和他说的话自相矛盾。 |
on the other hand:另一方面; contradicts:v.反驳;驳斥;批驳;相矛盾;相反;(contradict的第三人称单数)
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So this is great— 5 and 4 could be the override code, but how do we know it's the only one? |
那好,五和四可能就是密码, 但我们怎么才能确定是唯一一个? |
which would be 1+5, 2+4, or 1+2+3, giving B 5, 8, or 6, respectively . |
也就是一加五,二加四, 或者一加二加三, B的数字分别就是五,八,或六。 |
If B had 5, he’d know that A had 6. |
B的数字如果是五, 他就会知道A的数字是六。 |
And if he had 8, the possibilities for A would be 2+4 and 1+2+4. |
他的数字如果是八的话, |
Only 6 is on the list of possible sums, so B would again know that A had 6. |
只有六是有可能的和数之一, 所以B就又知道A的数字是六了。 |
respectively:adv.分别地;各自地,独自地;
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To summarize , if A had 6, he still wouldn’t know whether B had 5 or 8. |
总结一下,A的数字如果是六, 他也不知道B的数字是五还是八。 |
That contradicts the second half of what B said, and 5 and 4 must be the correct codes. |
这就与B说的话的后半段自相矛盾了, 所以五和四一定就是正确的密码。 |
With seconds to spare you override the missile launch, shoot yourself out of the torpedo bay, and send the sub to the bottom of the ocean. |
以几秒之差,你阻止了导弹发射, 从鱼雷舱里射出去, 还有让潜艇沉没到了海底。 |
summarize:v.总结;概述;概括;归纳; spare:v.节约,吝惜;饶恕;分出,分让;adj.多余的;瘦的;少量的;n.剩余;备用零件; torpedo:n.鱼雷;v.用鱼雷袭击(或击沉);彻底破坏,完全摧毁;
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