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More of a logic problem, but strictly speaking, you could simplify this into boolean algebra which is math.

12 people say the following statements one after another:

#1: There are no honest people in this room;

#2: There is at most one honest person in this room;

#3: There are at most two honest people in this room

.. .. .. .. ..
#12: There are no more than 11 honest people in this room.

How many honest people are in the room?

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

This post was edited by Hawkeye on Apr 06, 2006.

I probably need a better way of masking spoiler text.

In any case, There are six honest people.

Give me me the rationale, and I'll give you credit for solving.

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

The statements are like this:

#1: There are at most 0 honest people in this room;
#2: There is at most 1 honest person in this room;
#3: There are at most 2 honest people in this room
#4: There are at most 3 honest people in this room
#5: There are at most 4 honest people in this room
#6: There are at most 5 honest people in this room
#7: There are at most 6 honest people in this room
#8: There are at most 7 honest people in this room
#9: There are at most 8 honest people in this room
#10: There are at most 9 honest people in this room
#11: There are at most 10 honest people in this room
#12: There are at most 11 honest people in this room

As you can see from the full list above - if you pick a person from the list and assume that he is honest, all following people must be honest (preceding persons are dishonest.)

The cutoff is at person 7, where there are 6 honest people. IF #6 where honest, you'd have 7 honest total, which contradicts #6's statement. If #8 and onward were honest, you'd have 5 honest, but that fails to meet the requirements of #6.

This is the official solution, but I would prefer one of my alternates - all of them are honest but have a false belief of what is true. :)