OT : Here's a puzzle for all you snowbound folk

Snowbound, bored at work, whatever. Kept me amused for a couple of
hours :-)


The Wises Chat
Once, upon a time, it was a famous wise named Hasen Said. The people
named him "The Wise of the Wises". One day, while travelling in the
world, he arrived at a sultan's Court, where he was received with high
honour. The sultan treated him with food, lodged him and, one day,
said to him:
"I govern my country with the help of the Wises Chat, who is said to
gather the 12 wisest men in my country. However, can you put them to a
test so that they can succeed only if they are worthy of the honour I
give them?"

Hasen Said thought a bit and then said:

"All right, gather them."

When all the wises have been gathered, Hasen said to them:

"Oh, Wise Men, your king, the sultan, gathered you to show us all your
wisdom. The servants had put a box before everyone of you. All these
boxes are identical. Here, in my bag, I have twelve precious stones:
some of them are emeralds, the others are rubies. I invite everyone of
you to get out of this room, while I put one of these stones in his
box, so that everyone can see the others' stones, but he doesn't know
his own stone."

And Hasen invited the first of the Wises to leave off the room. He put
in his bag a ruby. After he returned, the second left and Hasen put in
his box an emerald. To the third, he put an emerald. And so on until
the last. When the last Wise returned, Hasen said to them:

"Everyone of you saw the others' stones, but he doesn't know his own
stone. If you are wises indeed, and if you trust your mind and your
eyes, nothing prevent you to carry out my wish: all of you who have
emeralds, come here and put your box to the sultan's feet."

Unfortunately, nobody comes. The sultan got then angry and ordered
that all his Wises Chat be banished from the Court, but Hasen stopped
him:

"Don't act rashly, Sir. Me too I would have done the same thing."

Ten minutes later, Hasen said to them again:

"All of you who have emeralds, come here and put your box at the
sultan's feet!"

The same silence, nobody came. Hasen repeated the same invitation
every ten minutes, and after an hour, some of the Wises raised up and
came to the sultan, who opened their boxes: they all contained
emeralds! He asked to see the others' boxes: there were all rubies.
And we have to say that while all this hour, the Wises didn't say
anything, they only thought.

"Oh, Sir, Hasen said to the sultan, you may be proud of your Wises
Chat. They are really wise men!" And saying them good bye, he left
them.

The story ends here, but we invite you to continue it, showing how
many emeralds Hasen had put into the Wises' boxes and how did they
find out what stone he owns...



-----------------------------------------------------------------

There _is_ enough information here.

I'll post the solution in a bit.

silangdon wrote:

There _is_ enough information here.

I'll post the solution in a bit.

Page down for spoiler response.

Tony






























'tis easy. Six rubies, six emeralds. All those who could see six
rubies and five emeralds must have an emerald. Otherwise the test is
unfair in that the same information is not available to all of the
contestants and some would be disadvantaged in the test. Suprised it
took them an hour to work it out.

Tony

"Tony Raven" wrote in message
...
silangdon wrote:

There _is_ enough information here. I'll post the solution in a bit.

Page down for spoiler response.

Tony






























'tis easy. Six rubies, six emeralds. All those who could see six rubies
and five emeralds must have an emerald. Otherwise the test is unfair in
that the same information is not available to all of the contestants and
some would be disadvantaged in the test. Suprised it took them an hour to
work it out.

Does it say there were six rubies and six emeralds? It just said some were
rubys and some emeralds. I could have been a 7 to 5 split for example.
Without knowing there were six of each it's not possible to work it out the
way you describe.

"silangdon" wrote in message
news

Snowbound, bored at work, whatever. Kept me amused for a couple of
hours :-)

"Oh, Wise Men, your king, the sultan, gathered you to show us all your
wisdom. The servants had put a box before everyone of you. All these
boxes are identical. Here, in my bag, I have twelve precious stones:
some of them are emeralds, the others are rubies. I invite everyone of
you to get out of this room, while I put one of these stones in his
box, so that everyone can see the others' stones, but he doesn't know
his own stone."

"Everyone of you saw the others' stones, but he doesn't know his own
stone. If you are wises indeed, and if you trust your mind and your
eyes, nothing prevent you to carry out my wish: all of you who have
emeralds, come here and put your box to the sultan's feet."

Easy peasy.

"You have an emerald. What do I have?"

Mark Hewitt composed the following;:
"Tony Raven" wrote in message
...
silangdon wrote:

There _is_ enough information here. I'll post the solution in a bit.

Page down for spoiler response.

Tony






























'tis easy. Six rubies, six emeralds. All those who could see six rubies
and five emeralds must have an emerald. Otherwise the test is unfair in
that the same information is not available to all of the contestants and
some would be disadvantaged in the test. Suprised it took them an hour
to work it out.

Does it say there were six rubies and six emeralds? It just said some were
rubys and some emeralds. I could have been a 7 to 5 split for example.
Without knowing there were six of each it's not possible to work it out
the way you describe.

I originally thought as TR did, but what got me against that was the
original distribution .. Ruby, Emerald, Emerald and so on ...

Maybe there are eleven emeralds and only one Ruby, though ICBW.

--
Paul ...
www.4x4prejudice.org
(8(|) Homer Rules ..... Doh !!!
ebay stuff Item No 5754626752

Danny@Kendal composed the following;:
"silangdon" wrote in message
news

Snowbound, bored at work, whatever. Kept me amused for a couple of
hours :-)

"Oh, Wise Men, your king, the sultan, gathered you to show us all your
wisdom. The servants had put a box before everyone of you. All these
boxes are identical. Here, in my bag, I have twelve precious stones:
some of them are emeralds, the others are rubies. I invite everyone of
you to get out of this room, while I put one of these stones in his
box, so that everyone can see the others' stones, but he doesn't know
his own stone."

"Everyone of you saw the others' stones, but he doesn't know his own
stone. If you are wises indeed, and if you trust your mind and your
eyes, nothing prevent you to carry out my wish: all of you who have
emeralds, come here and put your box to the sultan's feet."

Easy peasy.

"You have an emerald. What do I have?"

Bzzzt "And we have to say that while all this hour, the Wises didn't say
anything, they only thought"

--
Paul ...
www.4x4prejudice.org
(8(|) Homer Rules ..... Doh !!!
ebay stuff Item No 5754626752

On 24/2/05 12:58 pm, in article ,
"silangdon" wrote:


Snowbound, bored at work, whatever. Kept me amused for a couple of
hours :-)


The Wises Chat
Once, upon a time, it was a famous wise named Hasen Said. The people
named him "The Wise of the Wises". One day, while travelling in the
world, he arrived at a sultan's Court, where he was received with high
honour. The sultan treated him with food, lodged him and, one day,
said to him:
"I govern my country with the help of the Wises Chat, who is said to
gather the 12 wisest men in my country. However, can you put them to a
test so that they can succeed only if they are worthy of the honour I
give them?"

Hasen Said thought a bit and then said:

"All right, gather them."

When all the wises have been gathered, Hasen said to them:

"Oh, Wise Men, your king, the sultan, gathered you to show us all your
wisdom. The servants had put a box before everyone of you. All these
boxes are identical. Here, in my bag, I have twelve precious stones:
some of them are emeralds, the others are rubies. I invite everyone of
you to get out of this room, while I put one of these stones in his
box, so that everyone can see the others' stones, but he doesn't know
his own stone."

And Hasen invited the first of the Wises to leave off the room. He put
in his bag a ruby. After he returned, the second left and Hasen put in
his box an emerald. To the third, he put an emerald. And so on until
the last. When the last Wise returned, Hasen said to them:

"Everyone of you saw the others' stones, but he doesn't know his own
stone. If you are wises indeed, and if you trust your mind and your
eyes, nothing prevent you to carry out my wish: all of you who have
emeralds, come here and put your box to the sultan's feet."

Unfortunately, nobody comes. The sultan got then angry and ordered
that all his Wises Chat be banished from the Court, but Hasen stopped
him:

"Don't act rashly, Sir. Me too I would have done the same thing."

Ten minutes later, Hasen said to them again:

"All of you who have emeralds, come here and put your box at the
sultan's feet!"

The same silence, nobody came. Hasen repeated the same invitation
every ten minutes, and after an hour, some of the Wises raised up and
came to the sultan, who opened their boxes: they all contained
emeralds! He asked to see the others' boxes: there were all rubies.
And we have to say that while all this hour, the Wises didn't say
anything, they only thought.

"Oh, Sir, Hasen said to the sultan, you may be proud of your Wises
Chat. They are really wise men!" And saying them good bye, he left
them.

The story ends here, but we invite you to continue it, showing how
many emeralds Hasen had put into the Wises' boxes and how did they
find out what stone he owns...


If you take the 'and so on..' to refer to the placing of the emeralds then
only the first has a ruby, the rest have emeralds. The one with a ruby would
then know that, as all the others are emeralds, he has a ruby so would not
move. Can't see how the others work out that they have emeralds rather than
rubies unless they guess based on the pattern. Of course, if they presume
that there are at least two rubies, then no one would move.

Otherwise I am completely stumped.

...d

There _is_ enough information here.

Here goes. I think there are 4 rubies and 8 emeralds. The Wises must all
assume that the others are not idiots; and my assumption assumes that
there are at least two of each type of stone from the wording.

Emerald holders would take the following times to solve each possible
distribution. We'll look at it from the point of view of Ed, who holds
an emerald:

10r:2e - immediate (t=0). Ed can see 10r:1e, therefore must be holding
1e (assuming 11r:1e violates the initial conditions).

9r:3e - second iteration (t=10). Ed sees 9r:2e; if he were holding a
ruby, the distribution would be 10r:2e which can be solved first time.
As it wasn't, it must be 9r:3e and Ed is holding an emerald.

8r:4e - third iteration (t=20). Ed sees 8r:3e; if he were holding a
ruby, the distribution would be 9r:3e which would have been solved last
iteration. As it wasn't, it must be 8r:4e and Ed is holding an emerald.

7r:5e - fourth iteration (t=30). Ed sees 7r:4e; if he were holding a
ruby, the distribution would be 8r:4e which would have been solved last
iteration. As it wasn't, it must be 7r:5e and Ed is holding an emerald.

6r:6e - fifth iteration (t=40). Ed sees 6r:5e; if he were holding a
ruby, the distribution would be 7r:5e which would have been solved last
iteration. As it wasn't, it must be 6r:6e and Ed is holding an emerald.

5r:7e - sixth iteration (t=50). Ed sees 5r:6e; if he were holding a
ruby, the distribution would be 6r:6e which would have been solved last
iteration. As it wasn't, it must be 5r:7e and Ed is holding an emerald.

4r:8e - seventh iteration (t=60). Ed sees 4r:7e; if he were holding a
ruby, the distribution would be 5r:7e which would have been solved last
iteration. As it wasn't, it must be 4r:8e and Ed is holding an emerald.

Interestingly, the ruby holders know that they do not have an emerald
before the emerald holders know they do... I think.

--
Mark.
http://tranchant.plus.com/

On 24/2/05 2:10 pm, in article
, "Mark Tranchant"
wrote:

There _is_ enough information here.

Here goes. I think there are 4 rubies and 8 emeralds. The Wises must all
assume that the others are not idiots; and my assumption assumes that
there are at least two of each type of stone from the wording.

Emerald holders would take the following times to solve each possible
distribution. We'll look at it from the point of view of Ed, who holds
an emerald:

10r:2e - immediate (t=0). Ed can see 10r:1e, therefore must be holding
1e (assuming 11r:1e violates the initial conditions).

9r:3e - second iteration (t=10). Ed sees 9r:2e; if he were holding a
ruby, the distribution would be 10r:2e which can be solved first time.
As it wasn't, it must be 9r:3e and Ed is holding an emerald.

8r:4e - third iteration (t=20). Ed sees 8r:3e; if he were holding a
ruby, the distribution would be 9r:3e which would have been solved last
iteration. As it wasn't, it must be 8r:4e and Ed is holding an emerald.

7r:5e - fourth iteration (t=30). Ed sees 7r:4e; if he were holding a
ruby, the distribution would be 8r:4e which would have been solved last
iteration. As it wasn't, it must be 7r:5e and Ed is holding an emerald.

6r:6e - fifth iteration (t=40). Ed sees 6r:5e; if he were holding a
ruby, the distribution would be 7r:5e which would have been solved last
iteration. As it wasn't, it must be 6r:6e and Ed is holding an emerald.

5r:7e - sixth iteration (t=50). Ed sees 5r:6e; if he were holding a
ruby, the distribution would be 6r:6e which would have been solved last
iteration. As it wasn't, it must be 5r:7e and Ed is holding an emerald.

4r:8e - seventh iteration (t=60). Ed sees 4r:7e; if he were holding a
ruby, the distribution would be 5r:7e which would have been solved last
iteration. As it wasn't, it must be 4r:8e and Ed is holding an emerald.

Interestingly, the ruby holders know that they do not have an emerald
before the emerald holders know they do... I think.

It seems close. I think Ruby and Emerald holders know at the same time.
OOps, no they don't, emeralds know first.

1. If there is one emerald then the person with the emerald can only see
rubies so he gets up.
2. If noone got up, then there must be at least 2 emeralds. If the man can
see only one, then he knows that he has the second. And gets up.
3. If noone got up, then there are at least three emeralds..

Each man with an emerald gets up on the n+1 th iteration where n is the
number of emeralds he can see.

As the ruby holders can see n+1 emeralds, they would only get up on the
following iteration.

...d

David Martin wrote:

Each man with an emerald gets up on the n+1 th iteration where n is the
number of emeralds he can see.

As the ruby holders can see n+1 emeralds, they would only get up on the
following iteration.


That fails the test objectives though in that it requires the emerald
holders to be wise whereas the ruby holders don't need to have a clue.
As a result he would be making a false assumption that the ones who
didn't get up knew they shouldn't rather than they are just sitting
tight being unwise and not having yet worked it out. As he is the
Wisest of the wise he would not make such a simple mistake so that
answer must be incorrect. The only correct one can be six-six because
it is the only option where the information presented to each of them is
identical and therefore an equal test of their wisdom whether they get
up or not. Of course if they were really wise they would have worked it
out within minutes not hours. YMMV

Tony