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If the arrangement is

ABC or BAC

And

Only Anna doesn’t state her information.

Then:

Since if ABC, B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.

Or

If BAC they will know C is younger than A and is not in the middle. This reveals his position. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for C it can either be BAC or ABC in his eyes.

Then

Zorro is a good logician.

Zorro is a not good logician if the youngest be:

BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.

If the arrangement is

ABC or BAC

And

Only Alice doesn’t state her information.

Then:

Since if ABC, B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.

Or

If BAC they will know C is younger than A and is not in the middle. This reveals his position. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for C it can either be BAC or ABC in his eyes.

Then

Zorro is a good logician.

Zorro is a not good logician if the youngest be:

BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.

If the arrangement is

ABC or BAC

And

Anna doesn’t state her information.

Then:

Since if ABC, B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.

Or

If BAC they will know C is younger than A and is not in the middle. This reveals his position. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for C it can either be BAC or ABC in his eyes.

Then

Zorro is a good logician.

Zorro is a not good logician if the youngest be:

BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.

If the arrangement is

ABC or BAC

And

Only Anna doesn’t state her information.

Then:

Since if ABC, B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.

Or

If BAC they will know C is younger than A and is not in the middle. This reveals his position. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for C it can either be BAC or ABC in his eyes.

Then

Zorro is a good logician.

Zorro is a not good logician if the youngest be:

BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.

If the arrangement is

ABC or BAC

And

They were all logical.

Then:

Since if ABC then A is the oldest and does not state this. B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.

Or

If BAC they will know C is younger than A and is not in the middle. This reveals his position and A doesn’t reveal her information. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for C it can either be BAC or ABC in his eyes.

Then

Zorro is a good logician.

Zorro is a not good logician if the youngest be:

BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.

If the arrangement is

ABC or BAC

And

Anna doesn’t state her information.

Then:

Since if ABC, B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.

Or

If BAC they will know C is younger than A and is not in the middle. This reveals his position. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for C it can either be BAC or ABC in his eyes.

Then

Zorro is a good logician.

Zorro is a not good logician if the youngest be:

BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.