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

[Nasma]

You have ten piles of ten coins. One stack is known to be entirely counterfeit. A normal coin weighs 10g and a counterfeit coin weighs 11g. What is the minimum amount of weighings required to determine which pile is the fake one? How is this done?

Make one word by swapping around the letters in "new door"

A man walks one mile south, then one mile east, then one mile north, ends up where he started and shoots a bear. What colour is the bear?

The adventurers win a competition and it is now prize time. There are three locked chests, one of which contains ~insert kickass item~ while the other two are empty.
The group is then asked to choose which chest they would like to win. After this has been done, the person in charge opens one of the other two chests, showing it to be empty and eliminating it from the available choices. He then states "for only 100gp, I will let you change your choice to the other remaining chest". Should the adventurers take him up on his offer.

Spoiler

One weighing, put one coin from pile one, two coins from pile two, etc... on the scales. If the weight is one gram more than it should be, then it is the first pile, 2 grams more then it is the second pile...

"one word"

white, he was standing on the north pole. Please, noone point out that there are actually an infinate amount of places he could be standing close to the south pole.

Yes, if they change then there is two in three change of getting it right

 

[Pielorinho]

Saviomaegy got the answer to the murder riddle; Corinthi's answer, while close, changes the meaning of the word "friend" rather dramatically, as well as making the wife more an accessory than an actual murderer.

Daniel

 

[Mark]

Who would spend time creating a bunch of sliding rooms where opening the doors moves the rooms around? The builder is trying to protect something. Why give anyone even a small chance of finding it?

Because he needs to get beck in himself. Safes have combinations because the contents need to be personally accessible.

 

[Iron Sheep]

Corran:
If one of the numbers is a prime number >50, B would immediately know the numbers.

Why?

What this means is that if the number B is given has a prime number bigger than 50 in the factors, then that must be one of the two numbers, since any number greater than one times a number bigger than 50 will be a number bigger than 100.

For example, if the number B was told was 1846, then it factors as 2*13*71, and the numbers have to be 26 and 71, since the other two possibilities (142 and 13, and 923 and 2) have one number greater than 100.

Also, thanks Vyper for the explanation of what I was missing. That does make the problem somewhat more accessible, but I think I'd still want to use a computer to solve it!

Corran

 

[RingXero]

The adventurers win a competition and it is now prize time. There are three locked chests, one of which contains ~insert kickass item~ while the other two are empty.
The group is then asked to choose which chest they would like to win. After this has been done, the person in charge opens one of the other two chests, showing it to be empty and eliminating it from the available choices. He then states "for only 100gp, I will let you change your choice to the other remaining chest". Should the adventurers take him up on his offer.

I'm gonna have to see the math on this one, I can't see how your answer would be correct. I know it's the classic 'Let's Make a Deal' puzzle from our great friend Monty, but how do you get from a 1 in 3 then a 1 in 2 to a two in three chance?


RX

 

[ScotMart2000]

Mmmk I believe I have the answer. The rats when they looked in the reflection, they saw star(s). The fox, bear and owl were confused because they saw xof, raeb, and lwo, respectively. The dog, saw god. Thus making the rats no chance for the dog if animals became their reflections.

Correct Rith! Great job.

Math for the "Let's Make a Deal" Riddle...

The adventurers have 3 chests to choose from, but only one had real gold. Their initial guess had a 1 in 3 chance of being correct and a 2 in 3 chance of being incorrect. After they guess, the host eliminates an incorrect chest that they did not guess. So, if they guessed incorrectly the first time (a 2 in 3 chance), the remaining chest must be the correct one. Switching gives them the best odds of finding the gold.

Is this clear or am I just muddling things up some more?

-Scot

 

[PennStud77]

Correct Rith! Great job.

Math for the "Let's Make a Deal" Riddle...

The adventurers have 3 chests to choose from, but only one had real gold. Their initial guess had a 1 in 3 chance of being correct and a 2 in 3 chance of being incorrect. After they guess, the host eliminates an incorrect chest that they did not guess. So, if they guessed incorrectly the first time (a 2 in 3 chance), the remaining chest must be the correct one. Switching gives them the best odds of finding the gold.

Is this clear or am I just muddling things up some more?

-Scot

Once the third chest is shown to have no gold in it, there is a 1 in 2 chance of WHICHEVER chest they pick to be correct, this is absolutely regardless of which one they have already picked. Switching their choice and keeping the chest they have both have the same probability of being correct.

 

[RangerWickett]

And so no, they shouldn't pay $100 for having the exact same chance of success.

 

[ScotMart2000]

Once the third chest is shown to have no gold in it, there is a 1 in 2 chance of WHICHEVER chest they pick to be correct, this is absolutely regardless of which one they have already picked. Switching their choice and keeping the chest they have both have the same probability of being correct.

Label the chest A, B and C. We'll say the gold is in chest A. Here are the 3 possibilities if the characters switch their choice:

1. The adventurers pick chest A. The host reveals B is empty. The adventurers opt to switch their choice to C. They lose.
2. The adventurers pick chest B. The host reveals C is empty. The adventurers opt to switch their choice to A. They win.
3. The adventurers pick chest C. The host reveals B is empty. The adventurers opt to switch their choice to A. They win.

By switching, the adventurers win 2 out of 3 times. By keeping their original choice, they only win 1 out of 3 times.

This happens because the host always reveals an empty chest that the characters have not picked. So, if the characters pick an empty chest (2 out of 3 times they will), the host will have to remove the only other empty chest and leave the chest of treasure there for the characters to switch to.

I realize this is fairly anti-intuitive at first, but I think once the possibilities are laid out, you see why it works.

-Scot

 

[RingXero]

but 'not' choosing to switch is also a choice, so you have to include those:

1. The adventurers pick chest A. The host reveals B is empty. The adventurers opt to switch their choice to C. They lose.
2. The adventurers pick chest B. The host reveals C is empty. The adventurers opt to switch their choice to A. They win.
3. The adventurers pick chest C. The host reveals B is empty. The adventurers opt to switch their choice to A. They win.
4. The adventurers pick chest A. The host reveals B is empty. The adventurers don't opt to switch their choice to C. They win.
5. The adventurers pick chest B. The host reveals C is empty. The adventurers don't opt to switch their choice to A. They lose.
6. The adventurers pick chest C. The host reveals B is empty. The adventurers don't opt to switch their choice to A. They lose.

Three losses, three wins. Equal chance of both. No gain in switching, and if you do switch you lose 100g, so the best bet is not to switch at all.

RX