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

### #31

Posted 08 January 2008 - 01:51 AM

### #32

Posted 08 January 2008 - 06:25 PM Best Answer

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #33

Posted 08 January 2008 - 10:59 PM

### #34

Posted 09 January 2008 - 01:19 AM

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."

### #35

Posted 10 January 2008 - 10:24 AM

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!!

### #36

Posted 16 February 2008 - 04:54 AM

Probably not - you're only specifying parity of one of the types, not the sequence itself.

What if RED and BLACK were replaced with 0 and 1!!!!

Would the solution for this puzzle represent a newcompression technique, where one number at the beginning can make the rest of the series known? in other words, would this reduce file sizes?

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

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #37

Posted 19 February 2008 - 01:43 AM

### #38

Posted 19 February 2008 - 02:32 AM

### #39

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)!

### #40

Posted 19 February 2008 - 10:27 PM

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