Best...Puzzle...Ever....

[Vyper]

Pielorinho, you're on the right track! I'm impressed to get such a quick and good reply. Honestly, it took me much longer to get as far as you got.

Unfortunately 2 and 9 is not the answer.

As you showed, if the sum is 11, A can be certain that B cannot find out the numbers. (It isn't the only number with this property. 17, for example, is another one.)

Now, if A tells B that he knows that B cannot find out the numbers, B knows, that 9 and 2 must be the answer, since he got 18, and that can only be factored as 2*9 or 3*6. 3 and 6 is impossible, because 3+6=9, and that can also be the sum of the primes 2 and 7 (if both numbers are prime, B would immediately know them from the product). So B knows the numbers.

But ...

B has to work from that: once he finds out that A knows he couldn't solve it, then he has to look at the sums of the different factor-pairs he was given. We know that he was given either 18, 24, 28, or 30; now we have to see which of numbers can be factored in a way as to tell A that the problem is intractable.

It can't be 30, since 30 can also be factored 15*2 (as I said before, 17 is another number that allows A's statement). But 18, 24 and 28 are all possible factors, so A cannot know the numbers at this point.

So, 2 and 9 is not the correct solution.

 

[Pielorinho]

Ow, Vyper. My head hurts again.

I'm driving down to Chapel Hill tonight (a three hour tour) with two smart guys; I'll see if they have any insight, and will try to post again on Sunday or Monday.

Daniel

 

[kirinke]

I'm currently looking for a good air- and fire-related puzzles (not riddle) for my current campaign. The rope one in this thread was good, and I might use that, but I'd be interested in any other ones people may know.

Corran

well i have a good one.
You have been teleported in a room without any doors. There are three
basins. one is full of water. the other is full of elemental fire. The middle one is empty. There is a plaque with this riddle on it.

In order to get out, you must fill the middle bowl with fire-water.
but what is fire-water?

 

[RithTheAwakener]

You have been teleported in a room without any doors. There are three
basins. one is full of water. the other is full of elemental fire. The middle one is empty. There is a plaque with this riddle on it.

In order to get out, you must fill the middle bowl with fire-water.
but what is fire-water?

Steam? or alcohol


edit* color trouble

 

[am181d]

Can you guys figure out where to go?

Well, I'd hope that the polymorphed bear is the paladin, otherwise the puzzle wouldn't be solvable! The drummer has admitted that he doesn't always tell the truth, and the juggler lied by saying that wasn't so. If the polymorphed bear isn't the paladin, you don't know who you're looking for.

That said, the polymorphed bear HASN'T said where to go, but where NOT to go. My first instinct would be to look for a cook in town, since the bear never explicitly tells anyone to go anywhere. Barring that, I would assume you take The Mandolin Road to Castle Arc to find the cook. (The Juggler, as the Jester correctly points out, is the one who always lies.)

 

[Tuzenbach]

Well, I'd hope that the polymorphed bear is the paladin, otherwise the puzzle wouldn't be solvable! The drummer has admitted that he doesn't always tell the truth, and the juggler lied by saying that wasn't so. If the polymorphed bear isn't the paladin, you don't know who you're looking for.

That said, the polymorphed bear HASN'T said where to go, but where NOT to go. My first instinct would be to look for a cook in town, since the bear never explicitly tells anyone to go anywhere. Barring that, I would assume you take The Mandolin Road to Castle Arc to find the cook. (The Juggler, as the Jester correctly points out, is the one who always lies.)

I'd ask the Jester if he's the Jester.

Then I'd ask the Juggler if he's the Juggler.

And so on. Repeat with all of them at least 5 times until I was sure as to the validity of their responses. Hopefully, I'd be able to figure out who to ask and who not to ask for directions!

 

[Fieari]

Well, the problem with that is that said troupe has left, and you're now questioning the incompetant fool who questioned them previously. So you only have those questions and answers to work with.

Might be simpler to solve the 2nd puzzle instead? No one has given it a try so far... and I solved that one more easily than the first.

 

[der_kluge]

well i have a good one.
You have been teleported in a room without any doors. There are three
basins. one is full of water. the other is full of elemental fire. The middle one is empty. There is a plaque with this riddle on it.

In order to get out, you must fill the middle bowl with fire-water.
but what is fire-water?

Spoiler

Can you set the basin of fire below the basin of water to boil it, and take the empty one and turn it upside down to fill it with steam?

 

[der_kluge]

I have a question, I really liked Merak's locking doors puzzle. I'd *really* like to implement something like that in my game next weekend. However, fixing Merak's mistake, I'll make the doors all steel to avoid any stone shaping problems.

But, is there a way to make it tougher? As someone pointed out, two levers, and bam! - through. Anyone here smart enough to soup it up a bit so that it requires at least 4 or 5 sequences?

 

[Iron Sheep]

Here's a real tough one.

There are two persons, A and B. The evil villain (tm) has imprisoned them, and tells them:

"Tomorrow you will be executed, unless you are able to solve this riddle: I am thinking of two numbers, both greater than 1 and smaller than 100. I will tell A the sum of those numbers (X+Y) and B the product (X*Y). If anyone of you finds out the numbers, he is free. But don't give each other any hints!"

After the villain has told A the sum and B the product, both are silent. Some moments of careful thinking later, B confesses: "Sorry, I have no idea, what the numbers were." A says: "Yes, I already knew that you couldn't find them out." - "Did you", B says, "In this case, I know them now." - A replies: "Okay, now I know them, too."

And indeed, after this conversation (which didn't seem to contain any hints - or so the villain thought), both knew the right numbers.

How did they do that, and what were the numbers?

I hate these sorts of weird number fact problems, and I'm a mathematician! That probably explains why I'm not a number theorist, though. Analysing what the problem says:

Spoiler

B's first comment means that neither X nor Y is prime, otherwise B could simply factor and say the answer. So at least one of the numbers must be a composite number.

A's response means that no matter how you split the sum (X+Y) as a sum of two numbers A and B greater than 1 and less than 100 (so X+Y = A+B), you never have both numbers A and B prime at the same time, since then A couldn't already be sure that B didn't know the answer. For example, the sum couldn't be 12, since 5+7=12, and 5 and 7 are prime. However 11 does have this property, since 11 = 2+9 = 3+8 = 4+7 = 5+6. Call this property of a number (P).

B's second comment means that of all the possible ways of factoring the product only one of them has a sum with property (P).

A's second response means that of all the ways to pick A and B to give the same sum as (X+Y), only one of them has just one way of factoring to give a sum with property (P).

Having determined all that, it's just a matter of going through and exhausting all the possibilities until you find the right one. I threw my computer at the problem, since I didn't feel like using my brain too much, and got the following:

Spoiler

The numbers 4 and 13 are a solution. The number A is given is 17, and the number B is given is 52.

A knows that B can't immediately tell what the factors are, since 17 = 2+15 = 3+14 = 4+13 = 5+12 = 6+11 = 7+10 = 8+9, and none of those pairs of numbers are both prime.

The factorizations of 52 are 2*26 and 4*13. 2+26 = 28, but 28=11+17, which are prime, so A wouldn't have said what he did if the sum was 28.

Looking at the other possibilities of products from A's information we have:

2*15 = 30, with factors 2*15, 3*10, 5*6. Both 17 (=2+15) and 11 (=5+6) have property (P), so if the product was 30, B wouldn't have known which was right. So A knows the product isn't 30.

3*14 = 42, with factors 2*21, 3*14, 6*7. Both 23 (=2+23) and 17 (=4+13) have property (P), so A knows that the product isn't 42.

5*12 = 60, with factors 2*30, 3*20, 4*15, 5*12, 6*10. Both 23 (=3+20) and 17 (=4+13) have property (P), so A knows that the product isn't 60.

6*11 = 66, with factors 2*33, 3*22, 6*11. Both 35 (=2+33) and 17 (=4+13) have property (P), so A knows that the product isn't 66.

7*10 = 70, with factors 2*35, 5*14, 7*10. Both 37 (=2+35) and 17 (=4+13) have property (P), so A knows that the product isn't 70.

8*9 = 72, with factors 2*36, 3*24, 4*18, 6*12, 8*9. Both 27 (=3+24) and 17 (=4+13) have property (P), so A knows that the product isn't 72.

So the only way that B could have known the factors is if the product was 52, so A knows that the numbers are 4 and 13.

I think this one's a bit too tough (mainly because of the size of the solution space you need to search) to throw at your players, unless your players are members of a math olympiad team.

Of course there's probably some neat way of seeing the answer quickly.

Corran