Six brothers Al, Bob, Cal, Don, Elmer and Fred always take the same seat when they have their meals in the circular dinner table. The following figure displays their seat numbers.

           1
      6       2
      5       3
          4


The following is known:

• Bob's seat number is precisely 1 larger than that of Elmer's seat number.
• The seat of Don is separated from Al's seat by precisely one of the other brothers.
• Al's seat number is either 1 larger than or 1 smaller than Fred's seat number.
• The absolute difference of Cal's seat number from that of Bob's and the absolute difference of Cal's seat number from that of Don's are respectively either, 2 and 5; or, 5 and 2.

Determine the respective seat numbers of the six brothers.

From the given, (The absolute difference of Cal's seat number from that of Bob's and the absolute difference of Cal's seat number from that of Don's are respectively either, 2 and 5; or, 5 and 2.), it can be deduced that one of the following is true: [Question marks (?) indicate the value, with the givens as yet observed, are as yet unknown]

• Al's = ?, Bob's = 3, Cal's = 1, Don's = 6, Earl's = ?, Fred's = ?;
• Al's = ?, Bob's = 6, Cal's = 1, Don's = 3, Earl's = ?, Fred's = ?;
• Al's = ?, Bob's = 4, Cal's = 6, Don's = 1, Earl's = ?, Fred's = ?; or,
• Al's = ?, Bob's = 1, Cal's = 6, Don's = 4, Earl's = ?, Fred's = ?.

From the given, (Bob's seat number is precisely 1 larger than that of Elmer's seat number.), Bob's seat number can not be 1, leaving:

• Al's = ?, Bob's = 3, Cal's = 1, Don's = 6, Earl's = 2, Fred's = ?;
• Al's = ?, Bob's = 6, Cal's = 1, Don's = 3, Earl's = 5, Fred's = ?; or,
• Al's = ?, Bob's = 4, Cal's = 6, Don's = 1, Earl's = 3, Fred's = ?.

From the given, The seat of Don is separated from Al's seat by precisely one of the other brothers.), if Don's is 6, with Earl's as 2, Al's must be 4; if Don's is 1, with Earl's as 3, Al's must be 5; and, as Cal's is 1 and Earl's is 5 when Don's is 3, Don's can not be 3. Thus...:

• Al's = 4, Bob's = 3, Cal's = 1, Don's = 6, Earl's = 2, Fred's = 5; or
• Al's = 5, Bob's = 4, Cal's = 6, Don's = 1, Earl's = 3, Fred's = 2.

Finally, from the given (Al's seat number is either 1 larger or 1 smaller than Fred's seat number.), leaves only:

• Al's = 4, Bob's = 3, Cal's = 1, Don's = 6, Earl's = 2, Fred's = 5

Posted by Dej Mar on 2009-05-26 19:42:02