Missionaries and Cannibals...

I know... Many logical riddles are named this way..
Pardon if my english is unclear...
Four logicaly minded missionaries between which there
is undying hatred find themselves caught by a tribe of
ferocius cannibals. After some discussion the chieftain
and the shaman decide to let one of them go.
The prisoners are lined up in a que facing the same direction.
The chieftain explains to them that he will choose from seven
apples, 3 red and 4 green, one for each one of them to hold on his head so that the prisoners behind them in line can se the apples of
all in front of him. The deal being that the prisoner first to correctly
state the color of his own apple will be set free. To guess wrong
would lead to a painful death.
The apples get distributed.
After several hours of agonizing thought the missionary at the front of the queue confidently states 'my apple is green'. And is free to go home to his family...

Did he guess?

No, he didn't guess. He knows that
- the last in the row didn't see three reds in front of him, because he would have been in a hurry to declare he had a green one
- the second last, knowing the above, didn't see two reds in front of him because he would have been in a hurry to declare he had a green one
- the third last (i.e. the second in the row), knowing the above, didn't see a red in front of him because he would have been in a hurry to declare he had a green one
- so he correctly derived from it that he had a green apple.

Originally posted by Mephisto2
No, he didn't guess. He knows that
- the last in the row didn't see three reds in front of him, because he would have been in a hurry to declare he had a green one
- the second last, knowing the above, didn't see two reds in front of him because he would have been in a hurry to declare he had a green one
- the third last (i.e. the second in the row), ...[text shortened]... urry to declare he had a green one
- so he correctly derived from it that he had a green apple.

Or, perhaps... just perhaps... the last person in the row deliberately suppressed his knowledge, knowing full well that this would cause the others to make certain conclusions.

-Ray.

Originally posted by rgoudie
Or, perhaps... just perhaps... the last person in the row deliberately suppressed his knowledge, knowing full well that this would cause the others to make certain conclusions.

-Ray.

Yes... Missionaries do like to put it up to chance :-)

Though, the above is the answer I was looking for :-)

Originally posted by rgoudie
Or, perhaps... just perhaps... the last person in the row deliberately suppressed his knowledge, knowing full well that this would cause the others to make certain conclusions.

-Ray.

I thought of that too, but it would not be the logical thing to do. Because only one will be freed, so time is important. We know that all four were logic minded, then it is surprising even that the first in the row waited several hours, and not a few minutes.

but remember, these guys hate eachother.

Originally posted by fearlessleader
but remember, these guys hate eachother.

Because they hate each other, the scenario could not play out like that:

First guy looks at hats, knows that logically he can't tell, sees that guy on end is wearing a green hat and knows guy on end will work it out eventually - so logically he must immediately make a guess about his own hat colour to try to deny life to guy on end.

Second guy sits there, he knows that if first guy can work it then his sworn enemy will live, and he works out that if the first guy CAN't work it out then he will guess, so second guy's best chance is to make a guess first.

Likewise third and last guys must immediately make a guess. Hence thay all shout out random colours at exactly the same time.

Originally posted by iamatiger
Because they hate each other, the scenario could not play out like that:

First guy looks at hats, knows that logically he can't tell, sees that guy on end is wearing a green hat and knows guy on end will work it out eventually - so logically he must immediately make a guess about his own hat colour to try to deny life to guy on end.

Second guy sits ...[text shortened]... must immediately make a guess. Hence thay all shout out random colours at exactly the same time.

Very good... And of course very right...
That is sound gaming theory.


However... It is still technically wrong since the text that
describe the question tell us what happened, and it did not
involve random shouting.

Had the missionaries been as intelligent as you though they would have started shouting :-)
Well spotted though.

Originally posted by rgoudie
Or, perhaps... just perhaps... the last person in the row deliberately suppressed his knowledge, knowing full well that this would cause the others to make certain conclusions.

-Ray.

Surpressing the answer resulted in certain death of ONE of the others. By shouting the colour of his hat immedeately he ensures the death of all three others.

Originally posted by TheMaster37
Surpressing the answer resulted in certain death of ONE of the others. By shouting the colour of his hat immedeately he ensures the death of all three others.

Can't logical thinkers be a little insane? 😛

-Ray.