 |
navigation
previous puzzle
next puzzle
previous puzzle
next puzzle
Puzzle Thirteen - Fun With Visitors - Solution Page
Five Hogwarts students - Levitus, Madeleine, Nora, Oliver, and Pascal - are having some (questionable) fun with a visitor from the Ministry of Magic by telling her to guess what year they all are at Hogwarts. Each student, as it turns out, is in a different year of their Hogwarts studies. Each student gave one clue about what year they are - but only the second year and the fourth year students told the truth! The first year, third year, and fifth year students all lied. The poor visitor from the Ministry couldn't figure out what years they were - but can you?
Solution:
This one's hard!
Let's start with a couple of scenarios:
Let's say for a moment that Madeleine is a second year (which means she'd be telling the truth).
Her statement is Nora is one year behind her (clue 2). If Nora is one year behind Madeleine, Nora would be the first year student. We know, however, that the first year student lied - and Nora said that she hadn't been at Hogwarts as long as Oliver. If Nora were the first year student, her statement about Oliver being at Hogwarts longer would be true because she's the youngest - and it can't be true, because the first year student lies. So this means Nora cannot be the first year student, and in turn Madeleine cannot be the second year student.
Now let's say that Madeleine is the fourth year student (which again means that she'd be telling the truth).
This would make Nora the third year student. As the third year student, Nora would have to be lying, and since she's saying Oliver is older than she is, it would mean that Oliver would actually have to be younger than she is. So Oliver would have to be either the first or the second year student.
If he's the second year student he's got to be telling the truth - but he says there's a two year difference between him and Pascal, which would make Pascal the fourth year student - and in this scenario Madeleine is the fourth year student. So it doesn't work for Oliver to be the second year student.
If Oliver is the first year student, then he's got to be lying. He says there's a two year difference between himself and Pascal, which would make Pascal the third year student which in this scenario is Nora. So Oliver would be lying, which means the scenario still works. So now in the scenario either Pascal is the second year student and Levitus is in fifth year or the other way around. If Pascal is second year, then he's got to be telling the truth about there being a one year difference between Levitus and Nora - but Levitus and Nora would be third and fifth years, so that doesn't work. If Pascal is fifth year, then he's got to be lying about there being a one year difference between Levitus and Nora - but Levitus and Nora would be second and third years, and so Pascal's statement would be true! So Pascal cannot fit into either second or fifth year in this scenario. So this means that Oliver cannot be a first year student either.
If Oliver can't be either first or second year, Nora can't be third year, which means that Madeleine can't be fourth year. So our second scenario has fallen apart, too.
So both of the scenarios we started with (Madeleine as second year and Madeleine as fourth year) didn't work. So Madeleine has to be first, third, or fifth year - which also means that she has to be lying.
Knowing that Madeleine is lying allows us to figure out some things about Levitus' year. Levitus says there's a two year difference between him and Madeleine. If he's a second year student, he's got to be telling the truth, which would mean Madeleine would be the fourth year student (the scenario that already fell apart). Similarly, if he's a fourth year student, it would mean Madeleine's the second year student, the other scenario that fell apart.
So Levitus has to be first, third, or fifth year, just like Madeleine. And he has to be lying, too. If he's in third year, then Madeleine would have to be in first or fifth, either of which is two years away from third. That would make Levitus be telling the truth, and he can't be. So Levitus can't be third year either. This means that Levitus has to be first year with Madeleine fifth, or fifth year with Madeleine first.
Since the fifth year is either Levitus or Madeleine, Nora can't be in fourth year. In fourth year she'd have to be telling the truth, but she says Oliver is older. Oliver can't be in fifth year, so Nora can't be in fourth.
So let's say that Nora is in third year. She'd be lying about Oliver being older - and since the first year is either Levitus or Madeleine, the only place left for Oliver would be second year. The only year left is fourth year after placing Oliver in second, so Pascal would have to be fourth year in this scenario. Pascal would have to be telling the truth as a fourth year, and he says Levitus and Nora are one year apart. But Nora's third year, and Levitus is either first or fifth - so Pascal couldn't be telling the truth and this scenario falls apart - Nora can't be in third year.
The only year left for Nora is second year. She is thus telling the truth. This puts Oliver and Pascal in third year and fourth year one way or another. But since they're one year apart no matter which way they end up, Oliver's statement about there being a two year difference has to be a lie - which means he's the third year and Pascal the fourth.
If Pascal's the fourth year, he's telling the truth about there being a one year difference between Nora and Levitus. Because Nora's the second year, and Levitus can be either the first or the fifth, it means Levitus is the first year - which by process of elimination makes Madeleine the fifth year.
Whew!
To sum up:
- Levitus said, "There's a two year difference between Madeleine's year and my own."
- Madeleine said, "Nora is exactly one year behind me at Hogwarts."
- Nora said, "Oliver's been at Hogwarts longer than I have."
- Oliver said, "There's a two year difference between Pascal's year and my own."
- Pascal said, "There's a one year difference between Levitus and Nora's years in school."
Solution:
This one's hard!
Let's start with a couple of scenarios:
Let's say for a moment that Madeleine is a second year (which means she'd be telling the truth).
Her statement is Nora is one year behind her (clue 2). If Nora is one year behind Madeleine, Nora would be the first year student. We know, however, that the first year student lied - and Nora said that she hadn't been at Hogwarts as long as Oliver. If Nora were the first year student, her statement about Oliver being at Hogwarts longer would be true because she's the youngest - and it can't be true, because the first year student lies. So this means Nora cannot be the first year student, and in turn Madeleine cannot be the second year student.
Now let's say that Madeleine is the fourth year student (which again means that she'd be telling the truth).
This would make Nora the third year student. As the third year student, Nora would have to be lying, and since she's saying Oliver is older than she is, it would mean that Oliver would actually have to be younger than she is. So Oliver would have to be either the first or the second year student.
If he's the second year student he's got to be telling the truth - but he says there's a two year difference between him and Pascal, which would make Pascal the fourth year student - and in this scenario Madeleine is the fourth year student. So it doesn't work for Oliver to be the second year student.
If Oliver is the first year student, then he's got to be lying. He says there's a two year difference between himself and Pascal, which would make Pascal the third year student which in this scenario is Nora. So Oliver would be lying, which means the scenario still works. So now in the scenario either Pascal is the second year student and Levitus is in fifth year or the other way around. If Pascal is second year, then he's got to be telling the truth about there being a one year difference between Levitus and Nora - but Levitus and Nora would be third and fifth years, so that doesn't work. If Pascal is fifth year, then he's got to be lying about there being a one year difference between Levitus and Nora - but Levitus and Nora would be second and third years, and so Pascal's statement would be true! So Pascal cannot fit into either second or fifth year in this scenario. So this means that Oliver cannot be a first year student either.
If Oliver can't be either first or second year, Nora can't be third year, which means that Madeleine can't be fourth year. So our second scenario has fallen apart, too.
So both of the scenarios we started with (Madeleine as second year and Madeleine as fourth year) didn't work. So Madeleine has to be first, third, or fifth year - which also means that she has to be lying.
Knowing that Madeleine is lying allows us to figure out some things about Levitus' year. Levitus says there's a two year difference between him and Madeleine. If he's a second year student, he's got to be telling the truth, which would mean Madeleine would be the fourth year student (the scenario that already fell apart). Similarly, if he's a fourth year student, it would mean Madeleine's the second year student, the other scenario that fell apart.
So Levitus has to be first, third, or fifth year, just like Madeleine. And he has to be lying, too. If he's in third year, then Madeleine would have to be in first or fifth, either of which is two years away from third. That would make Levitus be telling the truth, and he can't be. So Levitus can't be third year either. This means that Levitus has to be first year with Madeleine fifth, or fifth year with Madeleine first.
Since the fifth year is either Levitus or Madeleine, Nora can't be in fourth year. In fourth year she'd have to be telling the truth, but she says Oliver is older. Oliver can't be in fifth year, so Nora can't be in fourth.
So let's say that Nora is in third year. She'd be lying about Oliver being older - and since the first year is either Levitus or Madeleine, the only place left for Oliver would be second year. The only year left is fourth year after placing Oliver in second, so Pascal would have to be fourth year in this scenario. Pascal would have to be telling the truth as a fourth year, and he says Levitus and Nora are one year apart. But Nora's third year, and Levitus is either first or fifth - so Pascal couldn't be telling the truth and this scenario falls apart - Nora can't be in third year.
The only year left for Nora is second year. She is thus telling the truth. This puts Oliver and Pascal in third year and fourth year one way or another. But since they're one year apart no matter which way they end up, Oliver's statement about there being a two year difference has to be a lie - which means he's the third year and Pascal the fourth.
If Pascal's the fourth year, he's telling the truth about there being a one year difference between Nora and Levitus. Because Nora's the second year, and Levitus can be either the first or the fifth, it means Levitus is the first year - which by process of elimination makes Madeleine the fifth year.
Whew!
To sum up:
|
1st year Levitus 2nd year Nora 3rd year Oliver 4th year Pascal 5th year Madeleine |
Puzzles and page copyright 2001 by Godrics Ghost (R '08).
All Harry Potter trademarks remain the property of their rightful owner.
All Harry Potter trademarks remain the property of their rightful owner.
