Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

Hats on a death row!! One of my favorites puzzles!


Best Answer bonanova, 08 January 2008 - 06:25 PM

Spoiler for Here's my idea
Go to the full post


  • Please log in to reply
471 replies to this topic

#31 unreality

unreality

    Senior Member

  • Members
  • PipPipPipPip
  • 6370 posts

Posted 08 January 2008 - 01:51 AM

There are so many answers which have been said to be "right" or "close to right" i'm confused... which is the right answer? at least the most right answer so far? You can just point me to whose post
  • 0

#32 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5887 posts
  • Gender:Male
  • Location:New York

Posted 08 January 2008 - 06:25 PM   Best Answer

Spoiler for Here's my idea

  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#33 unreality

unreality

    Senior Member

  • Members
  • PipPipPipPip
  • 6370 posts

Posted 08 January 2008 - 10:59 PM

Ah I see now! Awesome!
  • 0

#34 spoxjox

spoxjox

    Junior Member

  • Members
  • PipPip
  • 97 posts

Posted 09 January 2008 - 01:19 AM

bonanova cracks it out of the ballpark! Great job!

This is really fascinating to me. I consider myself a reasonably intelligent person, yet it took lots of hints and many tries by others before I stumbled upon a workable solution. Then, when the problem was made just a bit more general, my best solution was to keep two completely separate ideas in mind while you worked through the problem. It would have worked...but only if the prisoners had excellent memories and the ability to keep juggling two or three changing sums the whole time.

Then bonanova introduces what is, in effect, a simplified version of my solution -- and it's perfect! Easy (easier than my original, even), 100% effective, and works for any number of prisoners.

I wonder: What is it that allows people to step outside their own mental processes and see a result like this? When I read it, it's so obvious that, had I not tried to solve it myself, I would have perhaps assumed that it was easy, that surely I would have figured it out in a minute or so on my own. It takes real genius to say something new and to which hearers respond, "Yes, that's obvious."
  • 0

#35 roolstar

roolstar

    Advanced Member

  • Members
  • PipPipPip
  • 250 posts
  • Gender:Male

Posted 10 January 2008 - 10:24 AM

Good Job Bonanova (as usual), I always liked your way of thinking.

Now there's a thing about these kind of puzzles. For me, I enjoy the journey of finding the solution 10 times more than the analysis of the solution. And that's because I never know where I would end up!

And here's where this puzzle lead me:

What if RED and BLACK were replaced with 0 and 1!!!!
Would the solution for this puzzle represent a new compression technique, where one number at the beginning can make the rest of the series known? in other words, would this reduce file sizes?

I realise it needs a "little" adjustment but my intuition tells me there's something there....

Good job everyone!!
  • 0

#36 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5887 posts
  • Gender:Male
  • Location:New York

Posted 16 February 2008 - 04:54 AM

What if RED and BLACK were replaced with 0 and 1!!!!
Would the solution for this puzzle represent a new compression technique, where one number at the beginning can make the rest of the series known? in other words, would this reduce file sizes?

Probably not - you're only specifying parity of one of the types, not the sequence itself.
If you're interested, there's a simple compression technique called run-length coding;
starting with one of the values, you list the number of consecutive values in the string.

For example, [if red and black became 0 and 1] you might have 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0.
That would reduce to 3 2 1 4 3 1 2 2 1 1 4 2 1 3 2 reducing 32 values to 15.
Run length coding can be very efficient if the "runs" are long [tens or hundreds] but inefficient if there are many runs of length 1 and 2.

Data compression [and encryption] techniques are extremely interesting fields of study.
Check out Wikipedia here and here or do some Google searches on them.

- bn
  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#37 Sharpie357

Sharpie357

    Junior Member

  • Members
  • PipPip
  • 32 posts

Posted 19 February 2008 - 01:43 AM

YOU COULD JUST ASK YOUR OTHER CELLMATES, "WHAT COLOR IS MY HAT???" IF YOUR CELLMATES AREN'T SICK AND CRUEL, THEY WOULDN'T LIE, GUARANTEEING YOUR SURVIVAL.
  • 0

#38 Aatif

Aatif

    Junior Member

  • Members
  • PipPip
  • 72 posts

Posted 19 February 2008 - 02:32 AM

19 it is. With 20th having 50% probability.
Spoiler for Hats on the line

  • 0

#39 roolstar

roolstar

    Advanced Member

  • Members
  • PipPipPip
  • 250 posts
  • Gender:Male

Posted 19 February 2008 - 03:56 PM

Probably not - you're only specifying parity of one of the types, not the sequence itself.
If you're interested, there's a simple compression technique called run-length coding;
starting with one of the values, you list the number of consecutive values in the string.

For example, [if red and black became 0 and 1] you might have 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0.
That would reduce to 3 2 1 4 3 1 2 2 1 1 4 2 1 3 2 reducing 32 values to 15.
Run length coding can be very efficient if the "runs" are long [tens or hundreds] but inefficient if there are many runs of length 1 and 2.

Data compression [and encryption] techniques are extremely interesting fields of study.
Check out Wikipedia here and here or do some Google searches on them.

- bn


I agree...

In fact I gave up on the idea after the post since every prisoner has to count the ones in front of him to determine him/herself, which means replacing every 0 & 1 will still be another number (not very effective for compression I guess)!
  • 0

#40 unreality

unreality

    Senior Member

  • Members
  • PipPipPipPip
  • 6370 posts

Posted 19 February 2008 - 10:27 PM

This is an awesome riddle btw :D I voted 5 stars ;D
  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users