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[Shades]

Is this one 35, 45, 56, 69 btw?

Yes, very good. Would you care to explain why?

It's an every positive integer one.

1 (+2) 3 (+4) 7 (+5) 12 (+6) 18 (+8) 26 (+9) 35 (+10) 45 (+11) 56 (+13) 69

The next additions are +14 to +17 then +19 etc, 18 is skipped as it's already in the list, like 1, 3, 7 and 12 were.

[martinuzz]

Indeed.
It shares characteristics with a fractal, in that this string "shapes itself"
Let's call the string "[string x]

basically, [string x] starts at 1, and adds to that the next positive integer number from the [string off all positive integers, without those positive integers that are already present in [string x]]

Amazingly, if you want a computer to produce this string, it seems you need a logic formula of about 2 pages.

[Gatleos]

Heh, that was really good. How did a Dwarf who "isn't good with numbers" figure this out anyway?

[martinuzz]

Heh, that was really good. How did a Dwarf who "isn't good with numbers" figure this out anyway?

He didn't, this story is open-ended

[Gatleos]

Heh, that was really good. How did a Dwarf who "isn't good with numbers" figure this out anyway?

He didn't, this story is open-ended

Well, yeah. It wouldn't be much of a riddle if it wasn't. So does Shades get to come up with the next riddle then?

[Falc]

Amazingly, if you want a computer to produce this string, it seems you need a logic formula of about 2 pages.

Erm... No, you don't.

Python code:

Code: [Select]

>>> t = range(1,100)
>>> r = [0]
>>> for i in t:
        if i not in r:
                r.append(r[-1] + i)
>>> r
[0, 1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, 98, 114, 131, 150, 170, 191, 213, 236, 260, 285, 312, 340, 369, 399, 430, 462, 495, 529, 565, 602, 640, 679, 719, 760, 802, 845, 889, 935, 982, 1030, 1079, 1129, 1180, 1232, 1285, 1339, 1394, 1451, 1509, 1568, 1628, 1689, 1751, 1814, 1878, 1943, 2009, 2076, 2144, 2214, 2285, 2357, 2430, 2504, 2579, 2655, 2732, 2810, 2889, 2969, 3050, 3132, 3216, 3301, 3387, 3474, 3562, 3651, 3741, 3832, 3924, 4017, 4111, 4206, 4302, 4399, 4498]


[martinuzz]

I meant, without the help of any pre-defined operations.
Not code, but underlying logic formula. As in "From the collection of all positive integer numbers, you can form a string of numbers that makes up a collection of positive integer numbers which is used to form a string that is used to form the string bl etcbla"

Btw Python is great. I should learn it.

[QuakeIV]

Eh, python is simple looking at first, then it gets all screwy as things get more complicated.

[Maklak]

For the first riddle I'd go for a "brute force" approach. I just need a way of marking a dwarf (rise a hand, lie down, step away from others, whatever), and a question that has an obvious answer known to any dwarf, like "what rock am I holding in my hand", "Is magma hotter than ice", that sort of thing.

Line them up, and ask the question to everyone. Mark those who lied. We are left with either 3 of four dwarfs. Repeat procedure, untill left with one or 2. If 2 are left ask the same dwarf two such obvious questions. If he lies to one, the other one speaks the truth, and if he answers truthfully, ash him how to get out of forest.

This solution is as unimaginative as they get, but it would work in O(2D) questions, and that seems acceptable.

[expwnent]

I meant, without the help of any pre-defined operations.

Trivially, you can't do ANYTHING without pre-defined operations. At some point, there need to be primitive computations you can do.

[martinuzz]

For the first riddle I'd go for a "brute force" approach. I just need a way of marking a dwarf (rise a hand, lie down, step away from others, whatever), and a question that has an obvious answer known to any dwarf, like "what rock am I holding in my hand", "Is magma hotter than ice", that sort of thing.

Line them up, and ask the question to everyone. Mark those who lied. We are left with either 3 of four dwarfs. Repeat procedure, untill left with one or 2. If 2 are left ask the same dwarf two such obvious questions. If he lies to one, the other one speaks the truth, and if he answers truthfully, ash him how to get out of forest.

This solution is as unimaginative as they get, but it would work in O(2D) questions, and that seems acceptable.

That solution won't work, for you can only ask a total of 2 questions, to a single dwarf, as by the story. You cannot repeatedly ask the same questions to multiple dwarves.

[expwnent]

I believe I can solve the first riddle with just one question.

I assume that the dwarves are cursed to answer questions alternating between true answers and false answers, regardless of the knowledge or intelligence of the dwarf being questioned.

The question is:

If, after asking you this question, I ask you "how do we get out?", what answer could you not give me due to truth-speaking restrictions?

Truth-speaker reasoning:
Next time, I will have to answer the question falsely.
So I cannot answer the next question with the truth.
So for that question, I could not answer with the correct way out.
I am a truth-speaker right now, so I must answer truthfully and say the correct way out.

False-speaker reasoning:
Next time, I will have to answer the question truthfully.
I cannot answer the next question with falsehood.
If I answer this question with an incorrect way out, then I have answered it with the truth, because if I am asked that question next, I cannot answer with falsehood.
If I answer this question with the correct way out, then I have answered it with falsehood, because if I am asked that question next, I can, and must, answer it with the correct way out.
Therefore, I must answer the question with the correct way out.

So ask any one of the dwarves that question, then do what he/she says about how to get out.

If dwarves explode under these circumstances, because they don't know the correct way out and thus don't know if they're telling the truth, then instead ask a random dwarf

If, after asking you this question, I ask you "which of you knows the way out?", what answer could you not give me due to truth-speaking restrictions?

Then ask the dwarf who knows the way out the first question of this post.