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Puzzle Four - Quidditch Supplies - Solution Page
Demetrius, a third year student, went to Diagon Alley before the start of term. Like many Hogwarts students, he spent a lot of time at Quality Quidditch Supplies. He couldn't afford a new broomstick, of course, but there were four items that caught his eye: a broomstick care kit, a copy of Quidditch Through the Ages (signed by Ludo Bagman), a vintage program from the 1968 Quidditch World Cup, and a figurine of Victor Krum. Each of the objects was priced at a different multiple of 5 galleons - but none was more expensive than 25 galleons. Demetrius couldn't afford to buy all of them, but he did buy some. Can you figure out the order in which he saw the four objects (kit, book, program, figurine), how much each cost, and whether or not Demetrius bought them?
1. Demetrius paid 15 galleons for one of the items, which turned out to be his last purchase of the day. But he bought it before he'd seen the Krum figurine.
2. Demetrius bought both the most expensive and least expensive of the items he saw.
3. The broomstick kit cost 15 galleons more than the vintage program.
4. The first item Demetrius saw cost 5 galleons less than the fourth.
Solution:
Since every item costs a multiple of 5 galleons (but none is greater than 25 galleons), this means the possible prices are 5, 10, 15, 20, and 25 galleons. The broomstick kit cost 15 galleons more than the vintage program (clue 3). This will only be possible if the program and kit are 5 and 20 galleons, respectively, or if they're 10 and 25 respectively - these are the only two prices separated by 15 galleons.
Demetrius bought something worth 15 galleons (clue 1), and 15 galleons isn't a possible price for either the broomstick kit or the program. And we know he didn't buy the Krum figurine (clue 1). So the 15 galleon item must have been the book.
Since 15 galleons is in between either of the two possible prices for the broomstick kit and the program, the book could not have been either the most expensive nor the least expensive item Demetrius saw. Since he bought both the most expensive and the least expensive item (clue 2), that means that Demetrius had to have bought both the broomstick kit and the program (since he didn't buy the figurine). This also means that the broomstick kit was the most expensive item and the program the least expensive item.
The book was Demetrius' last purchase of the day (clue 1). Since he bought three items, and saw the Krum figurine after buying the book, the book must have been what Demetrius saw third and the Krum figurine fourth.
If the prices of the program and broomstick kit were 10 galleons and 25 galleons, the Krum figurine would have to be 20 galleons (because those two are the most expensive, all of the prices are different, and the 15 galleon price is already taken by the book). But we also know that the Krum figurine was fourth and that the first item is 5 galleons less than the fourth (clue 4). This would make the first item 15 galleons, which doesn't work because the book is the one that's 15 galleons and we know that's third.
So the only alternative is that the program and the broomstick kit are 5 galleons and 20 galleons, respectively. This would mean the Krum figurine would have to be 10 galleons, and since the first item was 5 galleons less than the fourth, the first item had to be the Quidditch program.
So:
| Order | Item | Price | Bought or Not? |
| First | 1968 Quidditch World Cup program | 5 Galleons | Bought |
| Second | Broomstick Kit | 20 Galleons | Bought |
| Third | Quidditch Through the Ages (signed) | 15 Galleons | Bought |
| Fourth | Viktor Krum Figurine | 10 Galleons | Did Not Buy |
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