free games
free game downloads

Reply
 
Thread Tools
Old 03-04-2010, 11:52 PM   #11
Steve
Administrator
 
Steve's Avatar
 
Join Date: Oct 2002
Location: London
Posts: 7,748
OK, I'm back with another theory. This is a bit of a sad theory as it requires the tallest person to sacrifice himself for the sake of the other 99. It also means the other 99 will have to be quick at mental maths to survive but if they can do the sums they can all make it out alive. This is probably not the actual correct answer, but it's took me a while to think it up so I thought I'd share it here:

The tallest guy can see 99 hats. He starts by counting all the black hats in front of him. Lets say he counts 46. This means he can also see 53 white hats. So he shouts out '53' and is instantly killed.

However, from their pre arranged strategy everyone knows the tallest guy will be calling out the number of white hats he counts. The other 99 now know that out of 99 hats there are 53 white.

So guy 99 counts all the white hats in front of him. If he counts 52 then he must be the 53rd white. If he counts 53 white then he is black.

Guy 98 listens to his answer. If it was white then he knows there are 52 white hats left. If it was black then he knows there are still 53 whites. He now counts all the whites in front of him and can workout his own color.

Guy 97 has also be listening carefully and depending on 99 and 98 answers he also knows how many whites are left, does the same count and calls out his color.

Providing everyone can hear all the answers everyone down the line should be able to to keep track of how many white hats are left and so workout their own color when it comes to their turn. This would allow 99 to live and put up a monument to the tallest man who saved them all.
Steve is offline   Reply With Quote
Old 03-05-2010, 12:41 PM   #12
xenocacia
Street Wise
 
Join Date: Feb 2010
Posts: 245
Steve, that is SO close that I'm very tempted to simply say that you are right! Try to improve your solution a little so that the tallest guy stands at least a 50% chance of survival! If need be, impose the restriction that if ANYONE says anything other than 'black' or 'white', they ALL die. The concept is very sound, though, it does require everyone to be counting furiously. So close!!
xenocacia is offline   Reply With Quote
Old 03-07-2010, 11:24 AM   #13
Steve
Administrator
 
Steve's Avatar
 
Join Date: Oct 2002
Location: London
Posts: 7,748
Think is certainly an interesting puzzle and good for getting the brain thinking.

For a valid solution the tallest guy is obviously going to have to say 'black' or 'white'. I assume he will say the color of hat on the 99th guy to give him a heads up but cannot see where to go from there? I'll try and explain:

Let's start with guy 100 saying white. He may or may not be right. Everyone else now knows guy 99 has white. Guy 99 now quickly counts all the white hats. Let say there are 60 including his own, leaving 39 black. He says white, is correct and goes free leaving 59 white hats.

Here's where I get stuck. Guy 98 can count all the remaining white hats and sees either 58 or 59, depending on what he is wearing. Say he counts 58 whites. How will he know he is wearing the 59th? He doesn't know there were 60/99 to start with. He might think there were 59/99 white to start with and he is wearing the 40th black. Make sense?

Can anyone shed some light on this?
Steve is offline   Reply With Quote
Old 03-07-2010, 11:27 AM   #14
xenocacia
Street Wise
 
Join Date: Feb 2010
Posts: 245
I certainly could. But really, Steve, you're terribly close! I could give you a very subtle hint. The NUMBER of hats each prisoner can see is not, in itself, all that important. All they really need to know is each time some one gets it right, there is ONE less hat... See where I'm going?
xenocacia is offline   Reply With Quote
Old 03-12-2010, 11:01 PM   #15
Steve
Administrator
 
Steve's Avatar
 
Join Date: Oct 2002
Location: London
Posts: 7,748


Been mulling this one over the last few days and still cannot see the light at the end of the tunnel. You got me xeno. Great puzzle though, hope someone else here posts the answer.
Steve is offline   Reply With Quote
Old 03-21-2010, 07:55 PM   #16
madmat
Novice
 
Join Date: Mar 2010
Location: Mumbai,India
Posts: 76
I think the origional description was right.You can find the minimum no,maximum can be anything from 51 to 100.The strategy they can decide is that every alternate man will tell the colour of the next persons hat.i.e.100th man will tell the colour of 99th man's hat.99th man will repeat the colour told by 100th man.Again 98th man will tell the color of the 97th man ...and so on.In this case 50 men will survive for sure.Out of the remaining 50,since there are only 2 colours hats,black & white ,the probability of their survival is 50%.So the answer according to me is minimum 50 and max 51 to 100.
madmat is offline   Reply With Quote
Old 03-22-2010, 04:21 PM   #17
xenocacia
Street Wise
 
Join Date: Feb 2010
Posts: 245
Nice try madmat, but that's not it. There is a surefire way to allow 99 people MINIMUM to survive, and its 50-50 on the last guy surviving. Do you want to mull over it some more?
xenocacia is offline   Reply With Quote
Old 03-23-2010, 04:12 AM   #18
madmat
Novice
 
Join Date: Mar 2010
Location: Mumbai,India
Posts: 76
O.k. I think I have got the solution,going further on Steve's line of thought.
100th man sees 99 hats.Out of 99 either black or white has to be even in number and the other colour odd.So they decide that if the colour is even in number 100th man will say "Its white" (or "Its black") if its odd he will just say white.
Lets assume there are 60 white and 39 black hats.So the 100th man says "Its white".99th will say white.that means the98th person will know that now both black and white hats are in odd no,he will count the black and white hats in front of him and whichever colour is in even no he will tell that colour.Lets say he says black,now the 97th person will know that now the white hats are in odd number and black hats are in even no.He will count the hats and if white are in even number he will say white,or if black hats are in odd number he will say black.......and so on.In this case even the 100th man will have atleast 50% chance of survival.
madmat is offline   Reply With Quote
Old 03-23-2010, 07:54 PM   #19
Steve
Administrator
 
Steve's Avatar
 
Join Date: Oct 2002
Location: London
Posts: 7,748
Good thinking mat. Glad to have your help on this one, it defeated me.

BTW, this post didn't original show as it was flagged for moderation but none of the mods picked it up. A post gets flagged when a new members post contains certain words which triggers the filter (in this case it was a false positive). It done to counter spam. Don't worry though once you have made a couple more posts this won't happen anymore.
Steve is offline   Reply With Quote
Old 03-24-2010, 01:43 AM   #20
xenocacia
Street Wise
 
Join Date: Feb 2010
Posts: 245
Well done mat, that's absolutely right! I'm seriously impressed, looks like I'm going to have to source for much tougher puzzles for you...
xenocacia is offline   Reply With Quote
Reply

Share This Page

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
What are they thinking? flowerpetal General Chat 3 09-16-2009 01:45 PM
lateral thinking 2 paradoxno1 General Puzzles 2 04-25-2009 09:35 PM
I'm thinking again Debra3131 Word Games 2 04-24-2006 07:52 PM
I'm thinking Debra3131 Word Games 4 03-30-2006 12:33 AM
Logical hats Steve General Puzzles 15 02-01-2004 11:38 PM


All times are GMT +1. The time now is 06:24 AM.