A hardware shop has seven shelves which are numbered as 1 to 7 from the topmost shelf to the bottommost shelf. Different items are kept in these shelves viz., Paints, Fasteners, Tools, Hinges, Chains, Utensils and Pipes, but not necessarily in the same order. No two items are kept in the same shelf.
Four items are kept between Tools and Paints, where the former is kept above the latter.
| | Case 1 | Case 2 |
| Shelves | Items | Items |
| 1 | Tools | |
| 2 | | Tools |
| 3 | | |
| 4 | | |
| 5 | | |
| 6 | Paints | |
| 7 | | Paints |
Hinges are kept immediate below Pipes, which is kept below shelf 4.
Thus, case 1 is invalid.
| | Case 2 |
| Shelves | Items |
| 1 | |
| 2 | Tools |
| 3 | |
| 4 | |
| 5 | Pipes |
| 6 | Hinges |
| 7 | Paints |
Utensils are kept in an even-numbered shelf.
| | Case 2 |
| Shelves | Items |
| 1 | |
| 2 | Tools |
| 3 | |
| 4 | Utensils |
| 5 | Pipes |
| 6 | Hinges |
| 7 | Paints |
Chains are not kept in the topmost shelf.
Therefore, the final arrangement is:
| Shelves | Items |
| 1 | Fasteners |
| 2 | Tools |
| 3 | Chains |
| 4 | Utensils |
| 5 | Pipes |
| 6 | Hinges |
| 7 | Paints |
Four items are kept below Chains. Also four items are kept above shelf 5.
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