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  • A hostile artificial intelligence called NIM has taken over the world's computers.

  • You're the only person skilled enough to shut it down,

  • and you'll only have one chance.

  • You've broken into NIM's secret lab,

  • and now you're floating in a raft on top of 25 stories of electrified water.

  • You've rigged up a remote that can lower the water level

  • by ejecting it from grates in the sides of the room.

  • If you can lower the water level to 0,

  • you can hit the manual override,

  • shut NIM off,

  • and save the day.

  • However, the AI knows that you're here, and it can lower the water level, too,

  • by sucking it through a trapdoor at the bottom of the lab.

  • If NIM is the one to lower the water level to 0,

  • you'll be sucked out of the lab,

  • resulting in a failed mission.

  • Control over water drainage alternates between you and NIM,

  • and neither can skip a turn.

  • Each of you can lower the water level by exactly 1,

  • 3,

  • or 4 stories at a time.

  • Whoever gets the level exactly to 0 on their turn

  • will win this deadly duel.

  • Note that neither of you can lower the water below 0;

  • if the water level is at 2,

  • then the only move is to lower the water level 1 story.

  • You know that NIM has already computed all possible outcomes of the contest,

  • and will play in a way that maximizes its chance of success.

  • You go first.

  • How can you survive and shut off the artificial intelligence?

  • Pause here if you want to figure it out for yourself.

  • Answer in: 3

  • Answer in: 2

  • Answer in: 1

  • You can't leave anything up to chance - NIM will take any advantage it can get.

  • And you'll need to have a response to any possible move it makes.

  • The trick here is to start from where you want to end and work backwards.

  • You want to be the one to lower the water level to 0,

  • which means you need the water level to be at 1, 3, or 4

  • when control switches to you.

  • If the water level were at 2,

  • your only option would be to lower it 1 story,

  • which would lead to NIM making the winning move.

  • If we color code the water levels,

  • we can see a simple principle at play:

  • there arelosinglevels like 2,

  • where no matter what whoever starts their turn there does, they'll lose.

  • And there are winning levels, where whoever starts their turn there

  • can either win or leave their opponent with a losing level.

  • So not only are 1, 3, and 4 winning levels,

  • but so are 5 and 6,

  • since you can send your opponent to 2 from there.

  • What about 7?

  • From 7, all possible moves would send your opponent to a winning level,

  • making this another losing level.

  • And we can continue up the lab in this way.

  • If you start your turn 1, 3, or 4 levels above a losing level,

  • then you're at a winning level.

  • Otherwise, you're destined to lose.

  • You could continue like this all the way to level 25.

  • But as a shortcut,

  • you might notice that levels 8 through 11 are colored identically to 1 through 4.

  • Since a level's color is determined by the levels 1, 3, and 4 stories below it,

  • this means that level 12 will be the same color as level 5,

  • 13 will match 6,

  • 14 will match 7, and so on,

  • In particular, the losing levels will always be multiple of 7,

  • and two greater than multiples of 7.

  • Now, from your original starting level of 25,

  • you have to make sure your opponent starts on a losing level every single turn

  • if NIM starts on a winning level even once,

  • it's game over for you.

  • So your only choice on turn 1 is to lower the water level by 4 stories.

  • No matter what the AI does,

  • you can continue giving it losing levels

  • until you reach 0 and trigger the manual override.

  • And with that, the crisis is averted.

  • Now, back to a less stressful kind of surfing.

A hostile artificial intelligence called NIM has taken over the world's computers.

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B1 US TED-Ed level water losing winning opponent

Can you solve the rogue AI riddle? - Dan Finkel

  • 61 4
    ally.chang posted on 2020/02/03
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