1. Re: Logic challenge (a REALLY tough problem)
20/02/2002 12:58:02 PM, petelomax at blueyonder.co.uk wrote:
>
>>The Shortest is Bernard
>NOPE (and you were so close)
>>In ascending Height order we have Bernard, Charles and Anthony
>Likewise
>
>Pete
>
You have correctly indicated that I gave the wrong answers before. However it is
still true that
Charles is not fighting.
Here is my logic:
Assuming that only one is not fighting then we have only three possible
situations.
(1) A + B fighting, and C not fighting
(2) A + C fighting, and B not fighting
(3) B + C fighting, and A not fighting
Taking these one at a time and applying the clues I get this:
Assuming (1) then A + B are fighting, thus C is NOT a fighter.
Using clue #2 "The younger of Bernard and Charles is the shorter of the two
fighters."
The younger of B and C is a fighter. C is not a fighter.
==> Thus B is younger than C (fact #1).
Resolving the clue for B gives "B is the shorter of the two fighters".
==> Thus B is shorter than A (fact #2).
Using clue #3 "The taller of Anthony and Charles is the younger of the two
fighters."
The taller of A and C is a fighter. C is not a fighter.
==> Thus A is taller (not shorter) than C (fact #3).
Resolving the clue for A gives "A is the younger of the two fighters".
==> Thus A is younger than B (fact #4).
So at this point we have:
for Age...
fact#1 B < C
fact#4 A < B
thus...
fact#5 A < C
giving...
A < B < C
for Height...
fact#2 B < A
fact#3 A > C (or C <= A)
this means that if C = A then B < C, else if C < A then any of C=B, C<B or B<C
could be true.
giving...
B < C <= A or C < B < A
Using clue #1 "The shorter of Anthony and Bernard is the older of the two
fighters."
A and B are fighters. From fact#4 B is older than A, thus B must be shorter
than A. But we already
knew this from fact#2.
-------------
Assuming (2) then A + C are fighting, thus B is NOT a fighter.
Using clue #2 "The younger of Bernard and Charles is the shorter of the two
fighters."
The younger of B and C is a fighter. B is not a fighter.
==> Thus C is younger than B (fact #1).
Resolving the clue for C gives "C is the shorter of the two fighters".
==> Thus C is shorter than A (fact #2).
Using clue #1 "The shorter of Anthony and Bernard is the older of the two
fighters."
The shorter of A and B is a fighter. B is not a fighter.
==> Thus A is shorter than B (fact #3).
Resolving the clue for A gives "A is the older of the two fighters".
==> Thus A is older than C (fact #4).
So at this point we have:
for Age...
fact#1 C < B
fact#4 A > C ( or C <= A)
giving...
C < B <= A or C <= A < B
for Height...
fact#2 C < A
fact#3 A < B
giving...
C < A < B
Using clue #3 "The taller of Anthony and Charles is the younger of the two
fighters."
The taller of A and C is a fighter. A and C are fighters. Fact #2 gives that A
is taller than C.
Resolving the clue for A gives "A is the younger of the two fighters".
==> thus A must be younger than C.
however this contradicts fact#4.
Thus we can discard (2) which means that B must be fighting.
----------------------------------
Assuming (3) then B + C are fighting, thus A is NOT a fighter.
Using clue #1 "The shorter of Anthony and Bernard is the older of the two
fighters."
The shorter of A and B is a fighter. A is not a fighter.
==> thus B is shorter than A (fact#1)
resolving for B we get "B is the older of the two fighters"
==> thus B is older than C (fact#2)
Using clue #3 "The taller of Anthony and Charles is the younger of the two
fighters."
The taller of A and C is a fighter. A is NOT a fighter.
==> thus C is taller than A(fact#3).
resolving for C we get "C is the younger of the two fighters"
==> thus C is younger than B(fact#4).
Using clue #2 "The younger of Bernard and Charles is the shorter of the two
fighters."
B and C are bother fighters. Fact#4 gives us that C is younger than B.
Resolving for C we get "C is the shorter of the two fighters".
==> Thus C is shorter than A.
however this contradicts fact#3.
So we can disregard (3) thus A must be fighting.
Thus we have shown that A and B must be fighting so therefore C is not fighting.
Also, there is not enough information to resolve whether C is taller than B or
not, but A is the
youngest, then B then C is the oldest.
---------
Cheers,
Derek Parnell
