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# Marry the Princess

## Question

He had a lovely daughter, in age for marriage.

Weird King, decided to marry his daughter with the smartest Prisonner, as to know, YOU.

Find the right door and marry Natalia.

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Spoiler

For the puzzle, it must be assumed the following givens and inferences are fact.
The givens and inferences are:

• The Weird King is honorable and true to his word. He makes no false statements.
• The princess is Natalia, the daughter of the Weird King. Natalia is not a lion.
• There are two doors, and behind each is one cell. These two cells are separate areas that share no overlapping space.
• Natalia is in either the left or right cell, or in neither of the two cells. Natalia's occupancy does not extend to more than one cell.

If the first statement, the one on top, "Only one statement is true", was true, then each of the statements written beside the two cell doors would be false.

Enumerating the four statements:

1.       "Natalia is in this cell" – Natalia is in the cell behind the left door.

2.       "The lion is in the other cell" – A lion is the cell behind the right door.

3.       "One cell contains Natalia" – Natalia is in one of the two cells.

4.       "One cell contains a lion" – A lion is in one of the two cells.

Given that each of the four statements are false, from (1), Natalia is either in the cell behind the right door, or in none of the two cells,
from (2), there is a lion in cell behind the left door, or in none of the two cells; from (3), Natalia is in neither of the two cells; and, from (4), none of the two cells hold a lion. Thus, no cell contains Natalia or the lion. The Weird King has no intention that you die, but would choose to marry his daughter. Choosing the door on the right – as instructed by the given true statement "Find the right door and marry Natalia", would be then be the logical choice if you wanted to marry Natalia.

If the first statement on the top was not self-referential, but was factual, then only of of the four statements would be true.

• If (1.) is true, then Natalia is in the cell behind the left door; yet, then (3.), which must be false would be a contradiction by being true -- thus, (1.) is false.
• If (2.) is true, then the lion is in the cell behind the right door; yet, then (4.) which must be false would be a contradiction by being true -- thus, (2.) is false.
• If (3.) is true, then Natalia is in one of the two cells. As (1.) is false, Natalia must be in the cell behind the right door; and, as (4.) must be false, there be no lion in any of the two cells, which would be no contradiction for (2.) being false.
• If (4.) is true, then a lion is in one of the two cells. As (2.) is false, the lion must be in the cell behind the left door, and, as (3.) must be false, would then have Natalia absent from either cell, which would be no contradiction for (1.) being false.

As both (3) and (4) are still possibilities, choosing the door on the right would still result in not being consumed by a lion and would reveal either the princess or no princess being present, but nonetheless, as the Weird King's decision to have his daughter married, the choice of this door would be the only logical solution.

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Good point, I didn't evaluate the 4th statement being the only true one.

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Spoiler

Possibilities

1  L:Natalia  R:Empty  = true stat : 1,3
2  L:Lion     R:Empty  = True Stat : 2
3  L:Empty    R:Natalia = True Stat : 3
4  L:Empty    R:Lion   = True Stat : 2,4
5  L:Natalia  R:Lion   = True stat : 1,2,3,4
6  L:Lion     R:Natalia = true stat : 3,4
7  L:Lion     R:Lion   = true stat : 2,4
8  L:Empty    R:Empty  = True stat : none

Possibility number 2 and 3 are quailified
So choose right door, since you may find Natalia or empty room, at least you will not eaten by lion.

Edited by jasen
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Another consideration is the possibility that "Only one statement is true" is meant to refer to one statement of each of the pairs of statements. In such a case...

Spoiler

...Natalia is in the left cell and the right cell is empty -OR- a lion is in the right cell and the left cell is empty.
In this scenario, with "right" being opposed to "left", the phrase "open the right door and marry Natalia" becomes almost synomynous with "at death's door" and the only safe door to open is the door to the cell on the left with the princess being within it, or it being empty with no princess in either cell -- (unless the lion is a lioness and, as a daughter of the King of Beasts, is considered a princess).

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İ found ''the right door'' ! Now where's my princess ?

Spoiler
On 19.01.2016 at 11:29 PM, chinouii said:

He had a lovely daughter, in age for marriage.

Weird King, decided to marry his daughter with the smartest Prisonner, as to know, YOU.

Find THE RİGHT DOOR and marry Natalia.

Edited by denizcan

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wat

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funny, on my laptop i see no clues
on my iphone, i see a youtube video that gives clues. but i cant enter a spoiler on my iphone

the video posed a page with five lines of text and two doors

on top "only one sentence is true"

above left door, two sentences:
"Natalia is in this cell"
"The lion is in the other"

above right side, two sentences:
"one cell contains natalia"
"one cell contains a lion"

Spoiler

The first one says "Only one sentence is true"

If I believe it is one of the sentences, then all the others are false
that means either no cell contains natalia or both cells contain natalia.
If no cell contains natalia, then there's no point in picking a cell.
I think it must be false that both cells contain Natalia.

So, I believe that the first sentence "Only one sentence is true" is false.

That means we can look for a solution involving the other sentences, at least two being true.

Can "Natalia is in this cell" be true? It is consistent with "the lion is in the other", "one cell contains Natalia", andf "one cell contains a lion"
So this is a possible assignment: Natalia in left cell, lion in right cell.

Can "Natalia is in this cell" be false? If the right two sentences are true, then this is another possible assignment: Natalia in right cell, lion in left cell.

So, interpreting the first sentence as a self-referential sentence is not helpful; if true, it rules out the others, if false, it enables multiple valid interpretations.

If we just take the first sentence as referring ONLY to the four sentences below, which one can be the only true statement?

Natalia is in this cell. If true, it makes "one cell contains natalia" true as well". So this is false
"One cell contains Natalia". If true, then she must be in the right cell, to make the left statement false.
Also, there must be no lion at all, or else "one cell contains a lion" would be true.

So, Natalia is in the right cell, and there is no lion.

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