How to use logic?

Question

Explain how you would answer this question in detail.
Would you use logic or set up a formula?

Once upon a time there lived a beautiful princess named Rowena who wished to be married. Her father the king, not desiring her to wed, devised a test that a suitor must pass before being granted the hand of the princess. Before the man would be placed three boxes; one of gold, one of silver, and the third of lead. The potential groom had to correctly choose which of the three boxes contained a picture of the princess. There were inscriptions on the boxes as follows: on the gold box was written, “The picture is in me.”, on the silver box was written, “The picture is not in me.” and on the lead box was written, “The picture is not in the gold box.” The king would also give the young man a hint by saying, “Only one of the statements written on the boxes is true.” Which box contained the picture of the princess?

Answer 1

You can use logic to solve this by looking at the three statements in turn and the consequences if they are the only true statement.

If the gold box's statement "The picture is in me" is true, then the silver box's statement "the picture is not in me" is false, and you therefore have the picture in two places at once (gold box and silver box). So the true statement is not on the gold box.

If the silver box's statement "The picture is not in me" is true, then gold "picture is in me" is false, and the picture must be in the lead box. Similarly, the lead statement "not in the gold box" is false, so you have the picture being in both the lead and gold box. So the true statement is not on the silver box.

If the lead box's statement "the picture is not in the gold box" is true, then the gold statement "in me" is false, and so is the silver statement "not in me." This means the lead box's statement is true, and the picture is in the silver box.

Answer 2

as was already explained ---- one one statement is true

1 - The picture is in me (the gold box)
2 - The picture is not in me (the silver box)
3 - The picture is not in the gold box (the lead box)

Let us assume statement 1 is true
this means statement 2 and 3 have to be false
true - the picture is in me (the gold box)
so 2 must be false
false - the picture is not in me (the silver box)
this is a contradiction ... if state 1 is true, then statement two cannot be true

therefore statement 1 is false

So let us try statement 2 being true
true - "the picture is not in me" (silver box)
this means the picture is either in the gold box or lead box
so now assume statement 1 is false
false 1 - the picture is in me (gold box)
if this is false the picture must be in the lead box, and statement 3 must be fale
false 3 - The picture is not in the gold box
if this is false, it means that the picture is in the gold box .. but we already determined it could not be so their is a contradiction

Therefore statement 2 cannot be the true statement

So we have determined that statement 1 and statement 2 are both false, so statement 3 MUST be true

MUST BE TRUE 3 - "The picture is not in the gold box"
We now KNOW that the picture is in either the silver or lead box, and both 1 and 2 must be false
FALSE - 1 - The picture is in me (gold box) == YES this is false
FALSE - 2 - The picture is NOt in me (silver box) -- this has to be false which means that the picture actually IS in the silver box

So the answer is obviously that the picture of the princess is in the silver box

Easy enough?

Answer 3

I would draw a picture with each of the three scenarios:

Scenario1 :Gold Box has the pic

This means the following inscriptions are true:

Gold: True Silver: True Lead: False

Since this means two boxes are correct, this cannot be the right answer

Scenario 2: Silver Box has the pic

Gold: F Silver: F Lead: T

Here, only the lead box is correct, so this can be right

Scenario 3: Lead Box has the pic

G: F S: T L:T

Here, both the silver and lead boxes are correct, so this cannot be the right answer.

Answer 4

The only answer that fits is the picture is in the silver box. The too not inscriptions have more weight than the one positive.
The picture is in me is false
the picture is not in me is false
the picture is not in the gold box is true
so the picture is in the silver box