- #1
tonyjeffs
- 34
- 0
This is not a puzzle question exactly. It's a question about logic that the puzzle illustrates.
There are four dragons. It is known that dragons can have brown eyes but our four all have green eyes. They can see each others eyes, but don't know their own eye colour. They will turn into sparrows if they deduce that they have green eyes. They are safe so long as they don't know their eye colour, or if their eyes are brown. Their names are Angus, Ben, Carl and Dave.
Every dragon knows that every other dragon can plainly see at least two green eyed dragons
Every dragon must therefore know that every other dragon knows that there can not be more than two brown eyed dragons, and one of them must be himself.
Angus thinks "If I have brown eyes, which is possible, I'm safe, but if that is the case, Ben will be thinking "I can see Angus has brown eyes. If I also have brown eyes, that makes two of us, but that means Carl will think "I can see two dragons with brown eyes, Angus and Ben. If I have brown eyes too which is possible, that means Dave can see three dragons with brown eyes." " "
That nested "if" seems perfectly logical in its progression. Each individual step seem (to me) valid. Why does the third level of logically nested speculation give an impossible result. Clearly something is wrong with my (alleged) logic, but I can't get my head around exactly what is wrong. Can anyone grasp and describe the error?
From Angus's perspective, Ben, Carl and Dave have identical status and are therefore interchangeable.
From Angus's perspective of Ben's perspective, Carl and Dave are interchangeable.
Thanks
Tony
There are four dragons. It is known that dragons can have brown eyes but our four all have green eyes. They can see each others eyes, but don't know their own eye colour. They will turn into sparrows if they deduce that they have green eyes. They are safe so long as they don't know their eye colour, or if their eyes are brown. Their names are Angus, Ben, Carl and Dave.
Every dragon knows that every other dragon can plainly see at least two green eyed dragons
Every dragon must therefore know that every other dragon knows that there can not be more than two brown eyed dragons, and one of them must be himself.
Angus thinks "If I have brown eyes, which is possible, I'm safe, but if that is the case, Ben will be thinking "I can see Angus has brown eyes. If I also have brown eyes, that makes two of us, but that means Carl will think "I can see two dragons with brown eyes, Angus and Ben. If I have brown eyes too which is possible, that means Dave can see three dragons with brown eyes." " "
That nested "if" seems perfectly logical in its progression. Each individual step seem (to me) valid. Why does the third level of logically nested speculation give an impossible result. Clearly something is wrong with my (alleged) logic, but I can't get my head around exactly what is wrong. Can anyone grasp and describe the error?
From Angus's perspective, Ben, Carl and Dave have identical status and are therefore interchangeable.
From Angus's perspective of Ben's perspective, Carl and Dave are interchangeable.
Thanks
Tony