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Complicated Cars Conundrum (Posted on 2005-07-03) Difficulty: 3 of 5
Three cars entered the parking lot at the same time, and the attendant isn't quite sure about whose car is which. However, he knows that:

a. Cuthbert drove the BMW if and only if Mr. Cooper drove the Audi.
b. Albert drove the Cadillac if and only if Mr. Cooper drove the BMW.
c. Cuthbert is Mr. Brown if and only if Mr. Andrews drove the BMW.
d. Bert is Mr. Andrews if and only if Cuthbert drove the BMW.
e. Mr. Cooper drove the Audi if and only if Albert is Mr. Brown.
f. Cuthbert is Mr. Brown if and only if Albert drove the Cadillac.

Who arrived in which car?

See The Solution Submitted by Old Original Oskar!    
Rating: 1.6667 (3 votes)

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Tedious solution, redundant clue, a new challenge | Comment 3 of 7 |
So, eschewing Pennie's excellent insight, I decided to logic this puzzle out.  I get the following solution:

1) Assume Cuthbert is Mr. Brown.
    Then using (c), Mr. Andrews drove the BMW
     Using (f), Albert drove the caddy
     And then, using  (b) Mr. Cooper drove the BMW.

     But this is a contradiction!
         Cuthbert is not Mr. Brown
         Albert did not drive the Caddy
         Mr. Brown (not Andrews, not Cooper) drove the BMW.

     So far I've only used clues  (b), (c), (f)

2) Since Cuthbert is not Mr. Brown, he did not drive the BMW.
    Therefore, using (a) Mr. Cooper did not drive the Audi.
    Mr Cooper drove the Caddy and Mr. Andrews drove the Audi.

3) Therefore, using (e), Albert is not Mr. Brown. 
    We already know that Albert did not drive the Caddy,
    so Mr. Albert Andrews drove the Audi.

    and we already know that Cuthbert is not Mr. Brown,
    so  Mr. Cuthbert Cooper drove the Cadillac
    and Mr. Bert Brown drove the BMW.

    Penny's solution is the only one!
    And I never had to use clue (d)!

Challenge 1) Since the clues are redundant but not inconsistent, there are probably other subsets of clues which can be used to solve this problem.  Can you find a 5-clue subset other than the one I used that will do it?

Challenge 2) Is there some subset of four clues that is sufficient to solve this problem?   I haven't ruled it out!


  Posted by Steve Herman on 2005-07-03 15:17:29
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