OpenEuphoria

Re: Logic challenge (a REALLY tough problem)

• Posted by Derek Parnell <ddparnell at bigpond.com> Feb 19, 2002
• 453 views

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