Question 7
There are 42 beavers sharing 5 warehouses. The first beaver uses the first warehouse, the second uses the second, …, the fifth uses warehouse 5, the sixth uses the first warehouse, …, continuing to the last beaver.
One day the sixth warehouse is completed. The beavers now decide to share the warehouses as follows. The first beaver uses warehouse 1, the second warehouse 2, …, the sixth warehouse 6, the seventh warehouse 1, …, continuing to the last beaver.
| Warehouse | First beaver numbers with 5 warehouses | First beaver numbers with 6 warehouses |
|---|---|---|
| 1 | 1,6,11,… | 1,7,13,… |
| 2 | 2,7,12,… | 2,8,14,… |
| 3 | 3,8,13,… | 3,9,15,… |
| 4 | 4,9,14,… | 4,10,16,… |
| 5 | 5,10,15,… | 5,11,17,… |
| 6 | — | 6,12,18,… |
How many beavers still use the same warehouse as before?
One day the sixth warehouse is completed. The beavers now decide to share the warehouses as follows. The first beaver uses warehouse 1, the second warehouse 2, …, the sixth warehouse 6, the seventh warehouse 1, …, continuing to the last beaver.
| Warehouse | First beaver numbers with 5 warehouses | First beaver numbers with 6 warehouses |
|---|---|---|
| 1 | 1,6,11,… | 1,7,13,… |
| 2 | 2,7,12,… | 2,8,14,… |
| 3 | 3,8,13,… | 3,9,15,… |
| 4 | 4,9,14,… | 4,10,16,… |
| 5 | 5,10,15,… | 5,11,17,… |
| 6 | — | 6,12,18,… |
How many beavers still use the same warehouse as before?