# Day 5 The Inner Sanctum

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• Red Bottle

Proof:

Suppose the red bottle was made by Menes. Then at most one of the bottles is made by Menes, so that necessarily it is the red bottle. Therefore, The yellow and blue bottles were both made by Nil, so that both yellow and blue bottles contain the cure. This is of course a contradiction to the fact that the cure is only in one of the bottles. Therefore, the red bottle must have been made by Nil. Then since at least two of the bottles were made by Menes, those bottles must have been the yellow and blue bottles. It follows that the yellow and blue bottles do not contain the cure and hence, the red bottle contains the cure.

tldr us 20
• The cure is in the red bottle.

Nil's truth comes into play.

if it was true that The red bottle states at least 2 bottles were made by Menes ( and Menes always lies).

for 1 bottle to be truthful the other bottles must be lies. If Nil's statement is true on red bottle , the other 2 are lies which works for Nils and Menes.
if the yellow and blue bottle were true then it would have to be a nil's bottle since the bottle makes a true statement however it makes Menes owning the red bottle. Menes red bottle is a true statement and that does not work since Menes always lies.
• i believe the corect answer is the Red Bottle because Nil left a big clue inscribed on it, that 2 of the bottles were made by Menes (who always inscribed false statements), which means that the statements inscribed on the Yellow and Blue bottles are false statements.
• the red bottle has the cure. If Nil were to make the red bottle then that makes the other 2 diseases based on the knowledge that Menes lies and he would have made the other two bottles. This makes it certain that the red bottle contains the cure,
• If Menes (liar) wrote the Red Bottle inscription, then it is false and he only wrote one of the three, leaving the remaining two (yellow and blue) as true. This is impossible as the setup says only one is the cure.
---
Despite the statement that these two are the only ones who make the bottles, these 3 could have been made by one of them alone as it is not stated that they are definitively products of both.

If Menes alone made the bottles, then the red bottle is false, as well as the other two. In that case the cure is in the RED bottle.
Nil alone did not make the bottles as none of the statements agree.
---
If Nil (truth) wrote the inscription on the red bottle it is a true statement and Menes wrote the false yellow and Blue statements, making then NOT the cure. In that case the RED bottle holds the cure.

us20 Bent
• Red bottle The only possible case is that in which Menes writes lies on the labels of the bottles Yellow and Blue (The cure is here, which is false for both cases) and Nil writes something true in the bottle Red (At least two bottles of these bottles were written by Menes, which is true). By discarding the lies on the labels of the Yellow and Blue bottles, which tell us that in those two bottles there is no cure, we know that the cure is in the Red bottle.

ts20.travian.us

Seek the Truth, become Enlightened.
• There is one cure and two diseases.
Menes' statements are false
Nil's statements are true

Yellow Bottle (Y)
Statement: The cure is here
Opposite: The cure is not here

Blue Bottle (B)
Statement: The cure is here
Opposite: The cure is not here

Red Bottle (R)
Statement: At least two of these bottles were made by Menes --> At least two of these statements are false
Opposite: Fewer than two of these bottles were made by Menes --> At least two of these bottles were made by Nil --> At least two of these statements are true

The statements on the Yellow and Blue Bottles may both be false, but they cannot both be true, since there is only one cure.
Since Y's and B's statements cannot both be true, both of them cannot have been made by Nil, so at least one of the two was made by Menes.
If either Y's or B's statement is true, R's statement nullifies itself by reductio ad absurdum.
(Additionally, it is impossible by the statements given to make any distinction between Y's and B's contents)
Therefore, neither Y nor B can be true, and must have been made by Menes.
Therefore R is true, and the cure will be found in the Red Bottle, which was made by Nil.
• The red bottle contains the cure.

Nil made the red bottle, and wrote truly that Menes made at least two. Menes made the yellow and blue bottles, and wrote falsely that each contained the cure.

Any other combination requires either a) Menes writing the truth on at least one of his bottles, b) Nil writing a lie, or c) more than one bottle containing the cure.

Sjrg4, US2
• ### TLira wrote:

There is one cure and two diseases.
Menes' statements are false
Nil's statements are true

Yellow Bottle (Y)
Statement: The cure is here
Opposite: The cure is not here

Blue Bottle (B)
Statement: The cure is here
Opposite: The cure is not here

Red Bottle (R)
Statement: At least two of these bottles were made by Menes --> At least two of these statements are false
Opposite: Fewer than two of these bottles were made by Menes --> At least two of these bottles were made by Nil --> At least two of these statements are true

The statements on the Yellow and Blue Bottles may both be false, but they cannot both be true, since there is only one cure.
Since Y's and B's statements cannot both be true, both of them cannot have been made by Nil, so at least one of the two was made by Menes.
If either Y's or B's statement is true, R's statement nullifies itself by reductio ad absurdum.
(Additionally, it is impossible by the statements given to make any distinction between Y's and B's contents)
Therefore, neither Y nor B can be true, and must have been made by Menes.
Therefore R is true, and the cure will be found in the Red Bottle, which was made by Nil.

TLira, US 20
• Answer: The cure is in Red bottle
Explanation: There are 1 bottle containing the cure and 2 bottles of pure death. There is no statement of pure death on the bottles -> Nil made just one bottle and that bottle contains the cure. The other bottles were made by Menes -> the statement on Red bottle is true -> the Red bottle was made by Nil -> the Red bottle contains the cure.
• I don't see my answer here, so I am going to repost to make sure it's here.

USX fire and sand
ign: gdbubrocks

Start by assuming they are all false (made by menes).
We know this isn't possible, because the red bottle cannot be false in this case.

Now we know 1 or more bottles must be true.

Next assume all bottles are true.
This isn't possible because red says at least two bottles must be made by menes.

Now we know 1 or more bottles must be false.

Next assume exactly 2 bottles are true.
Both yellow and blue cannot be true because two bottles contain virus.
This would mean for 2 bottles to be true it would mean the red bottle must be true, which cannot happen.

Therefore we must have 2 false bottles, and 1 true bottle.
If the true bottle is yellow or blue, that would make the red bottle false, which isn't possible.

Therefore the true bottle must be red, and the yellow and blue bottles must be false.
This means the cure is in the red bottle.
• CONGRATULATIONS to our winners who were picked at random from all those with the correct answer for day 5 of the hero adventure.

TLira
Gr8
HockeyRat77

They each have won a voucher worth 60 gold which will be sent to your forum account.