Originally Answered: Insanely, impossible, and un-"google"able riddle?
i know this:
What a great problem! I had a fun time working on it. The solution
is certainly not obvious, in my opinion - that is part of what made
it so interesting. But, so that you, too, can enjoy the fun of
solving the problem yourself. I'll give you a few hints, and then you
can work on it. If after having worked on it more you are still stuck,
write back, and I can help more.
No. 1 No. 2 No. 3
a G D K
b G K D
c D K G
d D G K
e K D G
f K G D
2. Given a set of questions, we can, for each different way G, D, and
K are standing, determine what the answers to those questions will
be. For instance, suppose we were looking at the following set of
i. (To individual #1) Is G standing in the middle?
ii. (To individual #2) Is D to the left of G (assume, this is the
left from our perspective, not theirs. Thus, above in row f, K
is to the left of G and G is to the left of D and K is to the
left of D)?
iii. (To individual #3) Does D tell the truth?
Then, if G, D, and K are standing in order (a) where G is in the #1
spot, D is in the #2 spot, and K is in the #3 spot, then we will get
the following answers:
i. No. (G tells the truth, and the truth is that G isn't in the
ii. Yes. (D always lies, and the truth is that D is NOT to the left
iii. No or Yes (K could answer either way - K lies and tells the
So, the point of all of this is that, given a set of questions, we can
determine for each case a, b, c, d, e, and f, what the answers will
be. Our goal, then, is to come up with a set of questions such that
when we figure out what a, b, c, d, e, and f will say, they will all
be distinguishable from one another. So, does the above set of
questions work? In other words, could we have had a sequence of
answers No Yes No or No Yes Yes from one b, c, d, e, or f? Well, you
can look at b, c, d, e, and f, and discover that this wasn't really a
good set of questions. Row b might answer the same way row a
answered, and so, if we were to get the answers No Yes Yes, we
wouldn't know whether we had arrangement a or arrangement b.
So, we need to search for a better set of questions. How can we do
that? Well, certainly one way to do that is trial and error. Think
of three questions you think might give you enough information to
figure out who's who. This is a method that will sometimes randomly
work, but if you are like me, you probably won't be lucky enough to
happen upon the solution, so perhaps a further analysis of the problem
is needed. Let's make some more observations:
3. Your three questions CAN depend on previous answers. Thus, your
rule for asking three questions might be something like the following:
First, ask question a. If the answer to question a is yes, then ask
question by. If the answer to question a is no, then ask question bn.
Now do the same thing for question c - let it depend on question b's
So, the following scheme sums it all up:
a -- yes -- by -- yes -- cyy
a -- yes -- by -- no -- cyn
a -- no -- bn -- yes -- cny
a -- no -- bn -- no -- cnn
So, the first line of the scheme indicates that if the answer to
question a is yes, ask by. If the answer to question by is yes, ask
Okay, this is very important, and will most likely help you come up
with a good set of three questions.
Okay, my observations are over. The neat thing about logic problems
like this is that there are lots of different ways to look at them.
No one way is "better" than another, so while my way works, you might
be able to come up with a different but also completely valid way of
doing the problem. Thus, I don't want to say a whole lot more. I
suggest you think about the above observations for a bit and see if
anything comes to you. Just in case you need an extra boost, I'll
just mention one more thing which you can look at now if you want or
later, after you have thought about what I've said above.
Think about your first question. Without loss of generality, we can
assume you will ask your first question of the person in the No.1
position. If the answer to the first question is yes, then we will
know a certain amount of information, and if it is no, we will know a
certain amount of information. Step back for a minute and don't worry
about what question you will ask. Try to figure out what you would
like the answers to be for the 6 different orderings, a through f.
Suppose that for your first question, ordering a will give you a yes,
ordering b will give you a yes, and ordering c will give you a yes,
and ordering d will give you a no. Because K i