Six sets of twins ( a boy and a girl in every case) made several errors in their history and geography examinations; and it was noted that every girl made precisely the same number of errors as her brother in the two subjects. Name each pair of siblings and their surname and work out how many mistakes each made in their history and geography examination papers.

1. The boy ( not Luke ) whose sister is Louella made more history errors than Sammy.
2. George did better in history than the boy surnamed O'Connell, who made either one more or one less geography error than the twins surnamed Dean.
3. Anne made either one more or one less geography error than Louella.
4. The twins who made 11 geography errors didn't make exactly 11 history errors.
5. David and his sister made either one more or one less mistake in the history exam than the twins who made 14 geography errors.
6 Edward and his sister did worse at history than the pair who made 15 geography errors. Edward made one more error in the geography exam than Luke.
7. The McCall twins didn't make one less history mistake than the Vole twins
8. Susan ( who made seven history errors ) made one less geography error than the girl who made one less history error than Anne.
9. The twins surnamed Waters made one more history mistake than the twins surnamed Seal, who made more geography errors than the McCall twins.
10. Gail made one more geography error than the girl who made one more history error than Louella.
11. Martin made either one more or one less geography error than his best friend and his sister, who made more history mistakes than Diane.
12. Wendy and her brother ( who didn't make a total of eight history mistakes ) didn't make as many errors in geography as George and his sister.

Brothers are - David, Edward, George, Luke, Martin & Sammy.
Sisters are - Anne, Diane, Gail, Louella, Susan & Wendy.
Surnames are- Dean, McCall, O'Connell, Seal, Vole & Waters.
Geography errors are - 10, 11, 12, 14, 15 & 16.
History errors are 6, 7, 8, 10, 11 & 12.

Well, at least in my head, there are several "layers" of logic that get applied to puzzles like these.  The first is just to sort out what has been explicitly stated in the clues.  In other words, if you were filling in one of those logic puzzle charts, this is what you could fill in right off the bat:

1. Luke is not Louella's brother.
1. Sammy is not Louella's brother.
1. Louella did not make 6 (the fewest) history errors.
1. Sammy did not make 12 (the most) history errors.

2. George is not surnamed O'Connell.
2. George did not make 12 history errors.
2. O'Connell did not make 6 history errors.

Note that the second part of the clue doesn't tell us anything useful yet.  It would appear that this may imply that George is not surnamed Dean, but if you read it carefully this is not necessarily true, so I'm leaving that assumption out for now.

3. Nothing useful yet.

4. Pretty clear - whoever had 11 history errors didn't have 11 geography errors.

5. David did not make 14 geography errors.

6. Edward did not make 15 geography errors.
6. Edward did not make 6 history errors.
6. Whoever made 15 geography errors did not make 12 history errors.
6. Edward did not make 10 or 14 geography errors.
6. Luke did not make 12, 14 or 16 geography errors.

7. Nothing useful yet.

8. Susan made 7 history errors (finally we learn something!)
8. Susan (and the person who made 7 history errors) did not make 12 or 16 geography errors.
8. Anne did not make 6, 8, or 10 history errors.

9. The Waters twins did not make 6 or 10 history errors.
9. The Seal twins did not make 8 or 12 history errors.
9. The Seal twins did not make 10 geography errors.
9. The McCall twins did not make 16 geography errors.

10. Gail did not make 10 or 14 geography errors.
10. Louella did not make 8 or 12 history errors.
10. Sammy did not make 11 history errors (from clue 1).

At this point, Louella did not make 6, 7, 8, or 12 history errors.  If Gail made 11 history errors, Louella must have made 10, which from clue 10 is not possible, so we can add:

10. Gail did not make 11 history errors.

11. Diane did not make 12 history errors.

Note again that this clue does not necessarily exclude the possibility of Martin and Diane being twins, so I am not making that assumption.

12. Wendy did not make 8 history errors.
12. Wendy is not George's sister.
12. Wendy did not make 16 geography errors.
12. George did not make 10 geography errors.



*Phew!*  Hopefully I didn't miss something in there, I typed this kind of fast.

Anyway, the next "layer" of logic to be applied would be the "if-then" type, which closely resembles guess-and-check.  For example, "If Anne made 12 history errors, then blah blah blah..." and you look for contradictions.  I haven't done that step yet.  I need to eat some dinner first. :)

(Edited to fix typos.)

Edited on April 17, 2006, 6:15 pm

Edited on April 17, 2006, 6:24 pm

Posted by tomarken on 2006-04-17 18:13:14