Lateral Thinking VIII and IX

[Sayumi]

Okay, after having a go at most of the Lateral Thinking problems posted here I guess it's time to contribute something myself 
Let's see how you go with these...

Lateral Thinking VIII
25monks live together in a monastery, but because they are very busy they only see each other at dinner which all of them eat together. The specialty of this monastery is that the monks are not allowed to talk-no matter what happens. One day a number of the monks get sick. All of them know that at least one-maybe even all of them, have this illness and that it will have to be treated by a doctor, but only the ones who are sick are allowed to take a day off work to go. The problem is that the only sign of the disease is, that you get purple spots in your face and since there are no mirrors or other reflecting surfaces around, the monks themselves don't know if they are sick or not.

Now this is what happened. All of the monks came to dinner every day, sat down in their usual seat, ate and left again. They didn't use sign language, write notes or communicate in any other way. This continued for a number of days. One day (all on the same day) all of the sick (and only the sick) monks went to the doctor. How did they find out  that they are sick?
I should mention though, that all of the monks are really good at lateral thinking.

Additional remarks:
-the disease does not spread further after the first outbreak.
-A monk will go to the doctor when he knows that he is sick.

(Don't think any of you would get this wrong but just in case: This story is not meant to be religiously offending or anything, I just couldn't think of something else- you could just as well make them little green men or something like that.)


Lateral Thinking IX
You are blindfolded and 10coins (all of them are the same) lie in front of you, 5 of them with heads up the other 5 with tails up but they are all mixed up and you can't feel or find out any other way which side is up on which coin.
The task is to make two groups of five coins with the same number of coins with heads up and with tails up in both groups. (You are allowed to turn around the coins of course.)

An example would be having 3coins with heads and 2coins with tails up in each group.

(Heads and tails- the different sides of a coin. The one with a picture-normally a portrait- on it is heads; the other one is tails. It doesn't really matter for this though-you can also imagine them being different colors.)


Note: I gave these two and another one (which I might post later on today or tomorrow) to ayw for a consistency check (he actually solved all three within a day-I still can't believe he actually did) because I had to translate them and invented part of the monk riddle and the story for the third one myself (I only remembered the general idea of the original problem, but not the full story). It might be that we still missed something so
Feel free to ask if you don't understand anything - I don't bite

EDIT: I've added a couple of logic questions- go and have a look at them on page2.

8.3.09:  More added on page3 

[Holmes]

Fist, I have to say: " Yeah! Sayumi´s turn!!!!!! "

You put Lateral Thinking and a Case, it would be good to be able to continue this.


Second, I´m not going to post an aswer yet, it was only to say what I said firstly. Hehe.

But, they are very good ones, but for me the coolest is still the one of the three men. (Lateral Thinking VII)

[S.H.]

Spoiler:

May be a stupid answer....because there is only one monk who got sick? 

[Sayumi]

The answer I'm looking for is actually more of a strategy. Once you get it  right you can answer the question for any number of sick monks. But S.H., your suggestion is a good starting point for working on the complete answer. I'm sure you'll work it out.

[tera]

Yay! First, I think I have a solution for LT IX:

Spoiler:

Separate them into two piles of 5 coins each, then flip over all the coins in one of the pile.

For LT VIII, a question - is the disease still contagious after the first outbreak?

[Sayumi]

Yay! First, I think I have a solution for LT IX:

Spoiler:

Separate them into two piles of 5 coins each, then flip over all the coins in one of the pile.

For LT VIII, a question - is the disease still contagious after the first outbreak?

Spoiler:

The answer is:...  CORRECT!!! 

As for your question: no it's not. I forgot to mention that

[tera]

Hooray! And while I was thinking, I came up with a possible solution for number viii too:

Spoiler:

As soon as all the sick monks are identified, they will leave at the end of dinner and go to the doctor.

After finishing their meals, as long as the monks see a monk with purple spots, they will leave the room one by one, until only healthy monks and one monk with spots remain. Then that last monk will know he has the disease.

In subsequent days, each monk who knows he is sick will be ignored in the elimination process but stay until the end of dinner. After ___ number of days, there will be one unidentified monk remaining (i.e, he does not know his own status), but if he is healthy, the sick monks will see only healthy monks remain, so all sick monks have been identified and will leave for the doctor's; otoh, if he is sick, healthy monks will start leaving first, so he will know he is sick, and thus all the sick monks will have been identified.

[Sayumi]

Spoiler:

No, not the correct answer.
1. In this case leaving the room in a specific order counts as communication.
2. The monks most would have to talk about this strategy at some point, otherwise they wouldn't know about the "leaving one by one until only one sick monk remains"part.
"...until only healthy monks and one monk with spots remain" - You would still have to modify that slightly, because the healthy monks would still see the sick monk and continue leaving until only one sick monk remains in the room.

Another note to VIII:
A monk will go to the doctor as soon as he knows he is sick.

[sstimson]

Got a question about your answer to the coin question. Now I know this is unlikely but say when you pick your two pills one is all heads and the other is all tails. if you

Spoiler:

turn over one pile

then you will either have all tails or all heads. That would not result in two piles of equal number of heads and tails in total.

Of Course the question ask for equal number in piles not total

Later

Never mind I see. These are the possibilties HHHHH, HHHHT, HHHTT, HHTTT, HTTTT, TTTTT

Spoiler:

Flipping any of the get to left overs:TTTTT, TTTTH, TTTHH, TTHHH, THHHH, HHHHH this you get the other pile exactly

To expand this puzzle same start but this time make 2 piles. one all heads and other all tails. You can still flip coins. How would you do this?

Anther question does a monk 'feel' sick?

[Sayumi]

Anther question does a monk 'feel' sick?

No, he doesn't.

[ayw]

To expand this puzzle same start but this time make 2 piles. one all heads and other all tails. You can still flip coins. How would you do this?

Interesting, but I think that's impossible. You need some form of feedback.

Let's say you could ask at any time whether there are more heads or tails or equal numbers facing up. How often would you have to ask and how would you manipulate the coins to get one pile of heads and one pile of tails? Assume of course that you can always distinguish two coins from their location when you're blindfolded.

[S.H.]

any hint on LTVIII?    dont even know where to start....

[ayw]

any hint on LTVIII?     dont even know where to start....

So, your start was not bad. We know that there is at least one sick monk. What if there was only one sick monk. What would all the other monks at dinner see and be able to deduce? What would that one sick monk see and be able to deduce?

ayw
p.p. Sayumi
 

[S.H.]

um...do the monks know the exact number of how many of them have this disease?

[ayw]

um...do the monks know the exact number of how many of them have this disease?

Nope, otherwise it would be easy

Next hint...

Spoiler:

So, after you have fully thought through my first hint above, consider what the monks would see and deduce if there were only 2 sick monks.

p.p. Sayumi