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| Twins and their mistakes (Posted on 2006-04-17) |
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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.
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Submitted by Salil
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Rating: 4.0000 (6 votes)
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Solution:
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Susan made seven history errors (clue 8) and no one made nine, so Anne made either 11 or 12. Louella didn't make six history errors ( 1), so (10) must have made either 10 or 11. If Louella made 11 and Anne made 12, then Susan made one less geography error than Louella (8) and Gail made one more than Anne (10). But then, since no one made 13 geography errors, clue 3 doesn't work. So Louella made 10 history errors. If Anne made 11 history errors, then Gail made one more geography error than Anne (10) and Susan made one less geography error than Louella (8). But again, since no one made 13 geography errors, clue 3 still doesn't work. So Anne made 12 history errors.
The twins with 11 errors made one more geography error than Susan (8) and one less than Gail (10), so Gail made 12 or 16 geography errors and Susan made 10 or 14 : while twins with 11 history errors made 11 or 15 geography errors. Thus those with 11 history errors made 15 geography errors (4), Gail made 16 geography errors and Susan made 14. Edward made 12 history errors (6) so is Anne's brother; Anne and her brother made either 10, 11 or 12 geography errors, so (6) made 11 or 12 and Luke and his sister made 10 or 11, ie one of them made 11. Luke's sister isn't Louella (1), so Luke made either six or eight history errors, as did David (5). Thus David's sister is Gail.
Anne made 11 geography errors (3), so Luke made 10 and Louella made 12. Sammy's sister is Susan (1). Wendy made 10 geography errors (12), so Diane made 15. Luke ( who is Wendy's brother) made six history errors (12), so David made eight. By elimination, Sammy made seven and so is Susan's brother. Martin's sister is Louella (11). Diane's brother is George. Edwards is surnamed O'conell (2) and the Dean girl is either Louella or Wendy ( 10 or 12 geography errors). The waters and seal twins (9) made either eight and seven history errors or else 11 and 10; so the Seal twins made 14 or 12 geography errors and the McCall twins made 10 or 12. If the Seal twins made 12 geography errors and the McCall twins made 10, then (above) the Dean twins are excluded. Thus Sammy's surname is Seal and David's is Waters. Diane's surname is Vole. Martin's isn't McCall(7), so must be Dean. Luke's is McCall.
Thus ( geography-history );
David - Gail - Waters - 16 -8;
Edwards - Anne - O'Connell - 11- 12;
George - Diane - Vole - 15 - 11;
Luke - Wendy - McCall - 10 - 6;
Martin - Louella - Dean - 12 -10;
Sammy - Susan - Seal - 14 - 7;
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