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?

77 comments

  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. Nonsense. Why would I count as a MORE dangerous opponent once my turn has ended? I can't shoot anymore. It's a 50:50 chance I get targeted at the end round whichever wand I choose. Nonsense.

  3. Better solution: Open the hidden compartment in the briefcase and take out the Wand of Chaining, which gives you a 5% chance of successfully casting a spell, and then has a 1% chance to arc chain that spell onto an additional target. Since you don't have to actually target both enemies, the wand is legal. You then intentionally miss with the wand. Since you have a 5% chance of succeeding, you therefore have a 95% chance of failing your spell and actually hitting a target. It will then chain at a 99% chance, giving you an overall 94% chance of eliminating both targets on the first turn. Conglaturation! You win!

  4. I said the baniker and attack stone lady before I knew you could pass, then I said get the baniker and pass when they finally told me the rules. Im counting this as a solve.

  5. How can you possibly have a 1.6% chance to win with using the Noether 9000 and miss on purpose?
    You will be targeted by everyone and not be alive, or be turned into a cat if the others also miss on purpose.

  6. This is like playing a board game and jumping off the board 😂. Yes, the rules don't say anything about that but games just don't work like that

  7. I would take the red apples 🍎 because the chance of getting two of them that are poisonous are very small so that’s what I would do

  8. I had a simmilar idea I though to use this first wand on my self it probably dont work and still if it would work I can cancell that spell because I cast the spell so this 2nd guy is going to cast spell on the 3rd guy if it doesnt work he will be turned into statue and it will be my turn I free my self and cast spell on the 3rd guy if it worked great if it dont well I think I will be great statue if the 2nd guy turned 3rd guy to fish the same you escape end cast again spell I think it would better worked with 2nd wand

  9. Green bowl of apples, because they said if you eat two apples, than you will die. But not if it’s just one apple. That gives me a more chance to live.

    Or I could just not eat the apples at all. I’m allergic

  10. This is just like the
    "What's green and has wheels"
    "Grass i lied about the wheels"
    It has an aspect that isn't specified

  11. Chance of dying in the first bowl:
    2/5*1/4 (chances of picking both poisonous apples)*3/3(picking one of the remaining apples)=0.1
    Chances of dying in the second bowl:
    3/5*2/4(picking two poisonous apples)=0.3

  12. As green apples bascket has 2 poisonous apples, the probability of being gone is 1/10 and red apples bascet has 3 poisonous apples, so the chances of being gone is 3/10… So Green bascket should be chosen

  13. I didn’t know about missing on purpose but i did pick the 60% wand and hoped to miss. But my logic was to win at round 2 so i was close

  14. for the apple riddle, if you pick the green one, there are three possibilities and only one kills you, making your chances of living 2/3, but if you pick the red one, there are also three possibilities, only one kills you, making your chances of living 2/3 again! It's not how many out of the apples are poisonous, it's about how many of you pick can be poisonous, with the exception of picking one poisonous apple because it takes two to kill you, not one, but the reason why it works like this is because it takes two to kill you, but no matter what, you pick none, one, or two poisonous apples, but two apples is always the most you can take, it doesn't matter because of this!

  15. basically what this I thought was: OH so if i chose: 1. the right wand, and 2. the right person, i will have a greater chance of success.

    but no, the correct answer was to MISS ON PURPOSE.
    that's like having three options, but hiding the fourth and correct answer so that the person wont know about it.

  16. 80% kill 90% wizard – lets see the answer 🤣

    Edit: wtf??? U didnt clarified you can miss on purpose !!!

    So yes, without that bending rules like in your answer 😳 the best chances are:
    Taking 80% wand and try to kill 90% wizard. If you kill her its 70% against your 80 % in yo7r way. If you don't succeed, 70% will attack her aswell. If he kills her, you have 80% chance of winning.
    There is ofcourse small chance neither of you or the other wizard kills her, but its still your best shot.

  17. I would pick the green apples because:
    If I eat a poison apple off the bat, there are three safe apples and one poison apple left. Thus, a 75% chance of survival. If I eat a safe one first, a 100% chance of survival. So, i have a 50% chance of either 75% or 100%. chance of survival. Leaving me with an 87.5% chance overall.
    I wouldn’t pick the red apples because:
    If I eat a poison apple off the bat, there are two safe apples and two poison apples left. Thus, a 50% chance of survival. If I eat a safe one first, a 100% chance of survival. So, I have a 50% chance of either 50% or 100% chance of survival. Leaving me with a 75% chance overall.

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