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.

The majority of the information provided surrounds the girls and history, so this is where I started.

Susan made 7 History errors (Clue 8)
Anne did not make 6, 8 or 10 history errors (Clue 8). She made 11 or 12
Louella did not make 6, 8 or 12 history errors (Clue 10) She made 10 or 11.

Assume Anne made one more history error than Louella. Then the un-named “girl” in Clue 8 (girl-8) is Louella, and she has 1 more geography error than Susan;  and the un-named “girl” in Clue 10 (girl-10) is Anne, and she has 1 less geography error than Gail.
This cannot be true because in Clue 3,  Anne and Louella are separated by 1 error in geography, and this would create a situation with 4 girls separated by 1 error in geography, which is not possible with the scores provided. Thus, my initial assumption that Anne made one more history error than Louella is incorrect. Therefore Anne made 12 history errors and Louella made 10 history errors.

From Clue 8 we see that girl-8 made 11 History errors, and from Clue 10, we see that girl-10 also made 11 History errors. Therefore these clues refer to the same girl (girl-A). Following this info to the geography section of the clues, Gail made one more error in geography than girl-A who made one more geography error than Susan. Thus Gail and Susan are 2 errors apart. This can only be true if girl-A made 11 or 15 geography errors. However, from Clue 3, we can eliminate 11 geography errors. Girl-A made 15 geography errors, Gail made 16, and Susan made 14.

From Clue 6 Edward made one more history error than Girl-A. He must have made 12 history errors and be Anne’s twin. 

Anne (and Edward) made 10, 11 or 12 geography errors. Anne has one more or less geography errors than Louella (Clue 3). Edward has one more geography error than Luke. Luke and Louella are not twins. Thus Edward (and Anne) made 11 geography errors, Luke made 10 and Louella made 12.

Luke is not Anne’s twin (12 history errors), girl-A’s twin (11 history errors), Louella’s twin (10 history errors) or Susan’s twin (7 history errors). Thus Luke made 6 or 8 history errors.

From Clue 5, David made one more or less history error than the person who made 14 geography errors (Susan). Thus David made 6 or 8 history errors.

From David and Luke having made 6 or 8 history errors, and Clue 1, Sammy made 7 history errors and is Susan’s twin.

The rest was filling in the blanks with the other clues. (Left to the reader)

Results
David and Gail Waters, 16 geography and 8 history errors
Edward and Anne O’Connell, 11 geography and 12 history errors
George and Diane Vole, 15 geography and 11 history errors
Luke and Wendy McCall, 10 geography and 6 history errors
Martin and Louella Dean, 12 geography and 10 history errors
Sammy and Susan Seal, 14 geography and 7 history errors

Hmmmm Sammy Seal, Martin Dean and Gail Waters. Nice names!

Posted by Leming on 2006-04-24 19:26:41