**Challenge #40 Result**

**Wow! So many responses were received to this puzzle....over 300. Many
strategies were attempted, and conflicting answers were offered, which makes for
excellent dialogue. The reply I selected was from Lauri Kultii, from Finland,
which I have included below. Thanks to all Zeno's Patrons who submitted answers,
and keep coming back to the Coffeehouse, where mental pleasures are welcomed!
The mind is a wonderful tool....Barnette**

**Here is the original problem, along with Lauri's response:**

**Challenge: One night at Zeno's a
Guinness-loving ale patron placed a bet that nobody in the Coffeehouse could
meet this challenge: First, she placed on a table two boxes labeled
"A" and "B". A sign on box A says "The sign on box B is
true and the bottle of Guinness is in box A". A sign on box B says
"The sign on box A is false and the Guinness is in box A". Assuming
there is a bottle of Guinness in one of the boxes, which box contains the
bottle? Can you figure it out from the information provided? Explain your
answer.**

**Response: city: Helsinki
country: FINLAND
comments: Let: 'p' stand for 'The sign on box B is true'
'q' stand for 'The bottle of Guinness is in box A'
'r' stand for 'The sign on box A is false'.
Now it can be shown that assuming Guinness to be in box A yields a contradiction
in every possible state of affairs.
So, let's assume: the Guinness is in box A.
Now we have just two possibilities concerning the status of sign on box A;
either the sign (the proposition the sign states) is true or it is false. Let's
consider each possibilities in turn.
1. If the sign on box A is true it states 'p AND q'. So, p is true. That is, the
sign on box B is true. It means that 'r AND q' is true. But 'r' means that sign
on box A is false which contradicts our assumption at the beginning of this
paragarph, namely that sign on box A is true.
2. What about if the sign on box A is false? Then either p or q or both should
be false. Let's examine all possibilities in turn.
i) 'p AND NOT-q'. NOT-q straightforwardly contradicts our very first assumption
that the Guinness is in box A.
ii) 'NOT-p AND q'. NOT-p means that sign on box B (that is 'r AND q') is false.
That can happen in three possible ways.
a) 'NOT-r AND q'. NOT-r contradicts our assumption at the beginning
of 2 (i.e. that sign on box A is false).
b) 'r AND NOT-q'. NOT-q contradicts our very first assumption that
Guinness is in box A.
c) 'NOT-r AND NOT-q'. Same as above.
iii) 'NOT-p AND NOT-q'. NOT-q again contradicting the very first assumption that
Guinness is in box A.
So, under assumption that Guinness is in box A a contradiction is inevitable.
So, we deduce that Guinness is in box B (as it was stated that Guinness is in
one of the boxes). (By the way, assuming that Guinness is in box B does not
yield contradiction in all possible states of affairs. I tried.)
Lauri Kultti
**