## Puzzle challenges!

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Inky
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### Re: Puzzle challenges!

It is exactly 1/7, because any of the 7 races is equally likely to be chosen. If you happened to get the 8th option which doesn't correspond to any race, you'd just keep repeating the process until you got one of the 7 valid combinations.
The probability that you won't be able to choose a race ever is going to be (1/8)N where N is the number of times you repeat the 3 coin flips, which has limit 0 as N gets large, so you're "guaranteed" to end up choosing a race eventually (i.e. this process ends in a finite amount of steps with probability 1).

EDIT: Probably a direct calculation is more clear.
Thinking of the different ways we could choose Race #1 (HHH), if TTT means repeat the 3 flips.
-We could get HHH the first time (the initial 3 flips). Probability 1/8
-We could get TTT on the first time, followed by HHH. Probability 1/8 * 1/8
-We could get TTT on the first two times, followed by HHH. Probability (1/8)3
etc.
So summing the infinite geometric series, the probability of getting Race #1 is 1/8 + (1/8)2 + (1/8)3 + ... = (1/8)/(1 - 1/8) = 1/7.
Ravana
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### Re: Puzzle challenges!

Well, int x at least. log2 7 would otherwise fit.
WTrawi
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### Re: Puzzle challenges!

Ravana wrote:...log2 7 would otherwise fit.
Yeah then we would have to throw the dice 2,807354922 times
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Inky
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### Re: Puzzle challenges!

I edited the post to clarify that.
Wtrawi I am curious to hear what your riddle is, don't keep us in suspense!
WTrawi
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### Re: Puzzle challenges!

Inky wrote:...don't keep us in suspense!
Right, I only didn't post it already because I wasn't the one who solved yours first (it was Samonella).

Okay, so this is a quite easy (at least according to some previous ones), but tricky riddle, the gates of Heaven and Hell:

You're standing in front of two gates, one of them is the gate of Heaven and the other one is the gate of Hell. Before each gates stands a guard: one of them is always lying and the other one always tells the truth (of course you don't know which one is telling the truth and you also don't know whether the lying or the truth-telling one is standing before Heaven's gate).

You have to ask ONE question from ONE of the guards, then enter a gate. What question would you ask to find out which gate is the one of Heaven?

(I hope I wrote down everything clear )
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Inky
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### Re: Puzzle challenges!

This seems to be the same question as one I posted earlier here.
Though in this case maybe you could avoid hypothetical questions by asking
Spoiler:
WTrawi
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### Re: Puzzle challenges!

Yes, the riddle is completely the same, I'm sorry for that (although I love your answer )
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WTrawi
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### Re: Puzzle challenges!

I'm not exactly sure about the game rules, but I don't want this thread to die, so here's another riddle (which I've checked and wasn't already said )

So, the thing is:

Four injured men chased by a hoard of barbarians get to a chasm with a swinging rope bridge across it. They have to get to the other side and cut the bridge's ropes to flee away.
However, the bridge is so old that it can hold only two people at the same time and it's midnight with dark clouds all over the sky and they've got only one lantern so the two people have to stick together because of the holes on the bridge.
The first man can cross the bridge in 1 minute, the second one in 2 minutes, the third in 5 minutes and the fourth one in 10 minutes. They have got 17 minutes before the barbarians reach them. How should they go through the bridge?
(only two people at the same time sticking together in 17 minutes)

(oh and also sorry for my language, I'm sure I've made many mistakes writing this )
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Jarom
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### Re: Puzzle challenges!

I probably got it. Easy as a riddle, but not trivial.
Spoiler:
WTrawi
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### Re: Puzzle challenges!

Jarom wrote:I probably got it. Easy as a riddle, but not trivial.
You indeed got it! And yep, easy riddle but I've had to think a few hours until it clicked... the reason why I posted it is rather because it is one of my very few favourite riddles (just like the two-gates one).

Your turn, show us what you've got!
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Jarom
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### Re: Puzzle challenges!

Since the Two Paths riddle was there (twice) I'd like to post my own riddle based on it.

The Nested Riddle

A merchant was travelling through the country, in which all citizens are either always telling the truth or always lying, when he encountered footpad and peasant on a crossroad. There were two ways from the crossroad besides the one he came from, one leading to the bogs and one leading to the city, but merchant didn't know which way leads where. Foodpad told him, that one of them always tells truth, and the other one lies, and the merchant can ask only one question to only one of them. After careful considering the rules he asked peasant: "Which way leads to the city?". Peasant showed him the way, then he went the other one.

The question is:
Why the way he had chosen led him to the bogs?
WTrawi
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### Re: Puzzle challenges!

I think I've got it, but the last riddle was posted by me so I'll put it in a spoiler section if you guys think that someone else should post the next one.
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Inky
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### Re: Puzzle challenges!

I think (?) the riddle is asking how it could be that the merchant actually ended up at the bogs, despite using the logic that WTrawi posted above which would make him conclude that the way to the city was the one the peasant didn't point to.

(Well if the merchant was really logical he wouldn't trust the chaotic footpad, and ask the nice lawful peasant )

Maybe the reason is that
Spoiler:
About posting new ones: I wouldn't worry about the rules too much, if no one has already posted a riddle I'd say that anyone is welcome to post theirs!
Jarom
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