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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 the world should blow itself up,the last audible voice would be an expert saying it can't be done

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 the world should blow itself up,the last audible voice would be an expert saying it can't be done

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. :)