So I've been listening to a podcast which has a bunch of puzzles on it. The podcast is old and the puzzles are even older but there are a few mixed in there that I'd not heard before and so I thought I'd share them.

All answers in spoilers please so that others can solve it independently

If you've heard it before then feel free to answer in spoilers but also state that you heard it before or heard similar before.

1). You are standing at 4:00 on a giant analogue clock. You flip an unfair coin that you know will come up heads x% of the time. If it comes up heads then you move clockwise 1 hour. If it comes up tails then you move anticlockwise 1 hour. What is the probability that you will visit all of the hours 1 - 11 before visiting hour 12?

2). You have a bag of coins. At least half of them are gold and the remainder are either brass or bronze. They all look and feel the same. You have a machine that will compare 2 coins and tell you if they are the same or different. The process of putting the coins through is instantaneous but once a coin goes through the machine the coin must wait 24 hours before it can be put through again. How long do you need before you can identify a gold coin with 100% certainty?

I might add more puzzles to this thread as I hear more good ones.

Happy puzzling...

Puzzle 2 seems unsolvable. A bag of 50 gold and 50 bronze coins complies with the requirements and there is no way to identify a gold coin. I assume there must be an additonal requirement, like brass and bronze both >0

I meant to say that at least 50% are gold and the remainder are a mix of brass and bronze

I'm a jigsaw man myself.

sup

Puzzles ITT

I am not sure how this is not dependant on the number of coins in the bag.

see spoiler

I mean it has to be dependent on the number of coins in the bag. I'm not following your max amount, I think it can be less.

This is my worst case (in my head anyway...lol)


If you are unlucky and start with the brass, it could go

brass and coin 2 - diff
brass and coin 3 - diff
brass and coin 4 -diff
brass and coin 5 - diff (stop now...cant be gold)

then go to bronze 1

bronze and coin 2 - same
bronze and coin 3 - diff
bronze and coin 4 - diff
bronze and coin 5 - diff
bronze and coin 6 - diff (stop now..cant be gold)

The 2nd bronze coin would run the same as above.

4+5+5+14 and the next coin in has to be gold..

Except we can throw out the coin that matched the bronze. So I think the max is 9, at least with that method.

EDIT: Also we only need 3 differents on the second comparison. So max is 8 with that method

Hint: It's not dependent on the number of coins in the bag

So then it isn't about number of scans, but about the time frame. Hmmm

yeah, coins can be put through the machine and you get results instantaneously, but you can't put the same coin through the machine until 24 hours has passed.

Sorry if that wasn't clear from the original puzzle

no it was clear, I just didnt pay enough attention to it

Coin problem

What happens when every pair you compare is different?

Well I mean you could have 2 brass 2 bronze 4 gold, and you pick up

gold brass
gold brass
gold bronze
gold bronze

gold>brass+bronze according to the puzzle

I am assuming there is at least 1 more gold than brass+bronze. Not sure from the OPs

OK, it could be the same, you probably have to rerun and compare coins you haven't compared before, by numbering them.

Off to work now, I think this should be enough for other people to completely solve it.

OP also hinted that the solution is not dependent on the number of coins. So if there are X coins, the answer is not a function of X.

Seems hard to believe. If you start with 4million gold coins, 2 mllion bronze and 2 million brass and you have the bad luck of comparing two of the same coins 4M times, I don't see how you can do better than continue wth 4M coins for the next run.