Puzzle challenges!

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Samonella
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Re: Puzzle challenges!

Post by Samonella »

Ravana is right! Here's my way of explaining it:
Spoiler:
Assuming no one else has one, I actually can post one more.

Delfador is deep beneath the Heart Mountains, searching for the Sceptre of Fire. To search more efficiently, he and the rest of Konrad's army have split into groups of nine, so Delfador is alone with 8 recruits.

They've been exploring tunnels for a while when they pass a large, ominous doorway. Thinking they may be on the right track, they hurry onward through a straight tunnel for twenty minutes. That's when they enter a large circular chamber from one of its four entrances. As luck would have it, one of the recruits stumbles on a trip wire, and sets a deadly spell in motion! The cave starts rumbling, and a booming voice announces that the cave, all the way back to the doorway, will collapse in one hour! Worse, the spell wipes the crews' memories of which entrance they came through, so the only way to determine which of the four exits is safe is to travel down it for 20 minutes until finding the doorway.

Delfador's immediate thought is to split the party up, exploring each path in 20 minutes, have everyone return to the center in another 20, and then all follow the team that found the exit to safety in the remaining 20 minutes. But there's a problem: Delfador senses that the curse has affected two of the recruits with a lying spell; though most of the time they will act normally, they might start telling lies at any moment. Being a powerful magician, he knows that he himself was not affected, but he can't tell which of the recruits were (or cure them) without several hours of investigation, so they will have to escape first.

Of course Delfador is a very clever man and immediately comes up with a plan that can still save all 9 people (himself and the 8 recruits) regardless of which ones were hit by the lying spell. But can you?
The last few months have been nothing but one big, painful reminder that TIMTLTW.

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Deciton_Reven
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Re: Puzzle challenges!

Post by Deciton_Reven »

Spoiler:
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Zap-Zarap
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Re: Puzzle challenges!

Post by Zap-Zarap »

I'd configure the teams in a different fashion than Deciton_Reven:
Spoiler:
Now he can deduct the correct way to go by logic from their answers, without any extra question (for names) needed.
Spoiler:
I didn't know this riddle, i solved it myself by thinking. :D
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Deciton_Reven
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Re: Puzzle challenges!

Post by Deciton_Reven »

Second Answer (Simpler)
Spoiler:
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Zap-Zarap
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Re: Puzzle challenges!

Post by Zap-Zarap »

A famous Vulcanian would call that answer "fascinating"...
But...
Spoiler:
Off Topic: I remember once playing a game of Ageless Scrolling Survival, with its maintainer and several others observing, and we started a chat discussion on how to spice up future versions of maps, when someone proposed to add some adventure game elements, like solving riddles to open doors and such... this thread could be a true goldmine for people that want to create something similar.
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Samonella
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Re: Puzzle challenges!

Post by Samonella »

I think Deciton_Reven's first answer works because of the way I worded the question, saying that they could "start lying," which implies that once they do they'll only tell lies. The original puzzle worded it differently, but you still solved this one so good job! Zap-Zarap found the officially right answer, and Deciton_Reven's second answer was the one I came up with when I tried to solve it. I think it works because the spell should only affect their spoken statements, not actions. But that is at least a little ambiguous, so Zap-Zarap's answer is the one Delfador used, just in case. :)
The last few months have been nothing but one big, painful reminder that TIMTLTW.

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Deciton_Reven
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Re: Puzzle challenges!

Post by Deciton_Reven »

Certainly. Sometimes it is very hard to create a riddle due to wording and a innocent word change in trying to flavor it changes the whole thing. I do think it's cool when you can get unexpected, or multiple correct answers for a puzzle. If whether any given thing they said was randomly a lie especially if it also extended to actions it would be very hard to decipher. You would be in real danger of sending people down tunnels and telling them to return if it was a dead end and have them just stay there and die.
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Inky
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Re: Puzzle challenges!

Post by Inky »

How about this:

You would like to choose at random from one of the 7 Wesnoth races to play. But ever since your red mage missed all their attacks that one time, you've had serious doubts about the Wesnoth "random" number generator. You don't trust computers and their "pseudo" random numbers anyway, so you've decided to do things the old fashioned way, with coin flipping.
Using your fair coin, how can you choose one of the 7 races with exactly 1/7 probability each?

p.s. Ephraim: You forgot to add a link to the colored hats riddle (a couple pages back) in the first post. By the way, appreciate your hard work in keeping it updated!
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Samonella
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Re: Puzzle challenges!

Post by Samonella »

I bet someone can come up with a more efficient way, but you could:
Spoiler:
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Zap-Zarap
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Re: Puzzle challenges!

Post by Zap-Zarap »

Binary Numbers to simulate a "dice" with 7 sides?
Spoiler:
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WTrawi
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Re: Puzzle challenges!

Post by WTrawi »

Yeah, I've also though of something similar as Zap-Zarap did:
Spoiler:
(btw Salmonella's method seems also 100% correct to me)
(oh and I've got an amazing riddle in my pocket if we run out of them :D)
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Inky
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Re: Puzzle challenges!

Post by Inky »

Yeah, everyone is correct, very nice! :D Wtrawi/zap-zarap's answer is the most efficient way but Samonella's method also works!
Samonella wrote:What's the expected number of coin flips that this method would take?
That's an interesting puzzle in itself! I can't think of a way to calculate it directly, but one way would be to use recursion: if E_k is the number of flips you still need if you see k heads, then E_1 = 0, you can calculate E_2 using E_1 (E_2 = 1/2*(2 + E_1) + 1/2*(2 + E_2) so E_2 = 4 I think), then you can find E_3 using E_2 and E_1, etc.
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Zap-Zarap
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Re: Puzzle challenges!

Post by Zap-Zarap »

Inky wrote:Yeah, everyone is correct.
....except me, sorry for my stupid answer, ofc there are 8 possible results (as in WTrawi's answer).

So, the solution must be a number of flips, that is 2x and be dividable by 7.
A simple calculation program should find that number easily, like:

Code: Select all

for (i=1; i<=10000000000000; i++) if (2^i)%7 == 0) print i;
Please adapt the syntax according to your favourite programming language, get a coin and and a few weeks of holidays and start flipping, i guess, the number will be quite large.
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Inky
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Re: Puzzle challenges!

Post by Inky »

Zap-zarap: your answer was basically correct! I assumed that since you didn't include TTH you just meant to throw that result out if you got it, which would be the same as wtrawi's method.
There's actually no x such that 7 divides 2x due to unique prime factorization, so what you want is the next highest power of 2.
(edit: I meant no integer x)
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Zap-Zarap
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Re: Puzzle challenges!

Post by Zap-Zarap »

Ok, but as you demanded
Inky wrote:exactly 1/7 probability each

..then there is no correct answer. :hmm:
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