Can you solve the wizard standoff riddle? – Dan Finkel

Can you solve the wizard standoff riddle? – Dan Finkel


You’ve been chosen as a champion
to represent your wizarding house in a deadly duel against
two rival magic schools. Your opponents are fearsome. From the Newt-niz school, a powerful sorcerer wields a wand
that can turn people into fish, but his spell only works 70% of the time. And from the Leib-ton school, an even more powerful enchantress wields
a wand that turns people to statues, and it works 90% of the time. Lots are drawn, and you’re chosen
to cast the first spell in the duel. The Newt-niz magician will go second, and the Leib-ton enchantress third, after which you’ll repeat casting in
that order until only one of you is left. The rules of magic duels are strict, and anyone who casts out of
order immediately forfeits the duel. Also, to prevent draws, the rules stipulate that
if everyone’s still standing at the end of the first round, you’ll all be turned into cats. Now, you must choose a wand. Your wizarding house presents you
with three options: the Bannekar, which binds
one target with vines and casts effectively 60% of the time, the Gaussian,
which turns one target into a tree and works 80% of the time, and the incredibly rare Noether 9000, which banishes one target
to a distant mountaintop and casts perfectly 100% of the time. Your opponents are masters of strategy,
as well as sorcery, and you know they’ll make the choices that
maximize their own chances of success. Which wand should you choose and what strategy should you employ to have the greatest chance
of winning the duel? Pause the video now if you want
to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 You reach for the Noether 9000 first. After all, it makes sense to enter
the duel with the most powerful wand. But before you pick it up, you consider
what would happen. As the most dangerous wizard, you’d also be the target
of the other two magicians, and you’d need to take
care of the most dangerous of them first. But afterward, there’s a 70% chance you’d
be struck down by the remaining wizard. That’s trouble. Maybe it’s better to take the Gaussian. It works 80% of the time, which means you wouldn’t be a target
until the enchantress was incapacitated. But if you succeeded in transforming her, you’d probably be turned
into a fish immediately after. If you transformed the sorcerer, the enchantress would almost
certainly turn you to stone. It would really be better if you missed. And that’s when you have an idea: what if you took the Gaussian,
then missed on purpose? Then, you would wait for the sorcerer
to attack the enchantress, and you’d have an 80% chance
of winning against the sorcerer. It’s a good idea, but there’s a problem; the sorcerer could also pass his turn and the enchantress, knowing that
she couldn’t pass without becoming a cat, would cast her spell on one of you. And since you’re the most dangerous
between you and the sorcerer, you’d be the target. And that’s when you see
what you really need to do: take the weakest wand, the Bannekar,
and miss on purpose. Now the sorcerer knows that
he’ll be targeted by the enchantress and he’ll have to try to turn her into
a fish to avoid being turned into stone. Seventy percent of the time he’d succeed and you’d have a 60% chance
of winning the duel at the beginning of the next round. If he fails, chances are he’ll be
turned to stone and you’d still have a 60% chance of
winning the duel against the enchantress. There’s a slim 3% chance
you’ll all be turned into cats, but when everything’s accounted for, you have better than even odds
of winning with this strategy. And that’s the best you can do. Here’s what the probability of winning
for the different strategies looks like. Who would’ve thought
that the best way to take your shot would be to throw away your shot?

Only registered users can comment.

  1. Sign up to be emailed the solution to the bonus riddle: https://brilliant.org/tededpoisonapples/! Also, the first 833 of you who sign up for a PREMIUM subscription will get 20% off the annual fee. Riddle on, riddlers!

  2. We all know the answer is to bring the Wand of Fireballs and turn them both into piles of ash. Wizards are notoriously bad at evading area damage.

  3. My Logic:

    1. Take the Noether 9000
    2. Cast on enchantress
    3. Cast again, illegally, on the other wizard
    4. Technically, you forfeited, so you lose. But no one else can win…
    5. To prevent a draw, you and the wizard who got out second, will fight
    6. As long as you go first in the rematch, you win!

  4. For the apple riddle you could eat half of four red apples and you would have technically ate 2 apples and if you ate the two poison ones you would have ate equivalent to 1 poison apple so you would still live

  5. you just have to choose the green apples because if u eat 1 poison AP then there are about 25% that u will eat the other poison AP
    if u choose the red bowl then if u eat one poison AP then there are about 50% that u will eat one of the other two poison AP

  6. Good riddle, I kinda thought everyone was turned into cats after first round regardless how many survived so i thought at first to take the 100% wand and cast it on himself to transport to safety or something like that the least probably kill wouldve been my second option but only because i thought missing it was 40 % not purposefully 100% .

  7. Wait so if you can miss can I just like… dodge someone else's shot, in that case I take the 100% wand and dodge the only shot that comes at me from the 70% guy. or is there an unwritten rule about shots that are aimed at someone not being able to be dodged.

  8. But it said that each wizard can’t go out of turn so would by getting the most powerful wand and getting rid of the second wizard be the most effective considering the third wizard would technically be going second?

  9. Pffffffft

    A: Missing on purpose was never given as an option. Can you block a spell too? Dodge? Shoot the ref? If the rules don't matter how can this be solved?

    B: The solution to the riddle is just a probability calculation which isn't a riddle, it's a math problem.

  10. All you people arguing that you shouldn't be able to miss on purpose… Uhm, the Bannekar wins either way guys….

  11. The real crime about this riddle is being given the set of rules and completely ignoring one of them. There is a rule that says, "after the FIRST round, they will ALL be turned into cats and they will ALL lose." There is a restriction on the number of turns, then, where the number of turns is limited to only 1. The solution of the riddle involves more than one turn, that is to say, it requires you to miss, have the other wizards take their turn at casting a spell, and then you go AGAIN. The solution is breaking one of the riddles' rules initially put forth. I would imagine that the moment the wizard decides to miss, his turn is over until the NEXT round. However, that is not the case as we can see here. He misses, the others take their turn, and he goes again all in the SAME turn. So when exactly does the turn end? In any case, either the wizard goes TWICE in the same turn, or he goes again on a different turn, and BOTH of these scenarios are misleading. One of the scenarios breaks the rules outright, while the other does not make it clear when a turn begins and ends. This is a bad riddle, terribly written.

  12. My answer was correct, but I did it for another reason. One of the rules are if you cast out of order, you forfeit, so if you choose the first wand, the 2nd wizard would be unable to cast a spell since he’s wrapped up, leaving the 3rd sorceress to have to cast and be forfeited from the tournament

  13. This makes no sense. It’s like if I said,

    “A car is going 80 miles per hour and the brakes are broken. You’re also locked in the car and have no tools in the car. How do you stop it?”

    And then the answer was, ”tHe cAr wAs aLmOsT aT eMpTy aNd rAn oUt oF gAs!!1!11”

  14. I wouldn't say that this is a bad riddle, but they stretched the unintuitivity a bit much in their "correct answer." I still find it interesting that the weakest wand is a good choice at all.

  15. If you choose the red bowl and eat two apples, meaning there are 20 different combinations of apples you could eat (5×4, total number of apples x apples you can choose with your current apple). Since there are 2 safe apples, and 3 unsafe apples, there is a 14/20 chance you will live, or 70% chance.

    I don’t have time to calculate the green bowl 🤪

  16. Green apple bowl is safer bet.
    There is 5 apples you have a 60% chance of getting a safe apple and a 40% chance of getting a poisonous apple.
    If your first apple is safe then your second Apple ( only 4 apples left) you have a 50% chance of getting a second safe apple or 50% for poisonous.
    -if your second apple is poisonous then on your 3rd Apple you have a 66.7% of a safe apple, but if your second apple is safe then it doesn’t matter what apple you eat because 1 Apple isn’t enough to kill you.
    If your first apple is poisonous then on your second apple you have a 75% of a safe apple and then on your third a 66.7% of a safe apple.
    Red bowl has the highest probability of you dying

  17. Green bowl:60% safe 40% poisonous3/5
    Red bowl:40%safe 60%poisonous2/5
    Eat 3 for Green Bowl2/5 R
    Eat 2 of Red Bowl3/5 R
    (Gb)3/5 x 2/5=(Rb)2/5 x 3/5
    So theyre both the same

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