Question 15
A beaver has 9 fir trees of three types (
), with 3 trees of each type. Trees of the same type have the same height, while different types have different heights. The beaver plants the 9 trees in a $3\times3$ garden so that each type occurs exactly once in each row and each column. At each position around the garden, the beaver puts a sign showing how many trees in the corresponding row or column can be seen from that position. Shorter trees behind taller trees are hidden. The illustration below gives an example of the signs for the arrangement shown.
Example-picture data, with rows top to bottom and columns left to right:
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | Short | Tall | Medium |
| 2 | Tall | Medium | Short |
| 3 | Medium | Short | Tall |
Numbers shown in the example:
| Viewing side | Row/column 1 | Row/column 2 | Row/column 3 |
| --- | --- | --- | --- |
| Left (rows) | 2 | 1 | 2 |
| Right (rows) | 2 | 3 | 1 |
| Top (columns) | 2 | 1 | 2 |
| Bottom (columns) | 2 | 3 | 1 |
The following diagram shows some signs already placed around the garden. What is the sum of all the numbers around the garden when all signs are in place?
Clues for the puzzle to solve; — means no number is given, not zero:
| Viewing side | Row/column 1 | Row/column 2 | Row/column 3 |
| --- | --- | --- | --- |
| Left (rows) | 3 | — | — |
| Right (rows) | — | 2 | — |
| Top (columns) | — | — | — |
| Bottom (columns) | 1 | — | — |
), with 3 trees of each type. Trees of the same type have the same height, while different types have different heights. The beaver plants the 9 trees in a $3\times3$ garden so that each type occurs exactly once in each row and each column. At each position around the garden, the beaver puts a sign showing how many trees in the corresponding row or column can be seen from that position. Shorter trees behind taller trees are hidden. The illustration below gives an example of the signs for the arrangement shown.Example-picture data, with rows top to bottom and columns left to right:
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | Short | Tall | Medium |
| 2 | Tall | Medium | Short |
| 3 | Medium | Short | Tall |
Numbers shown in the example:
| Viewing side | Row/column 1 | Row/column 2 | Row/column 3 |
| --- | --- | --- | --- |
| Left (rows) | 2 | 1 | 2 |
| Right (rows) | 2 | 3 | 1 |
| Top (columns) | 2 | 1 | 2 |
| Bottom (columns) | 2 | 3 | 1 |
The following diagram shows some signs already placed around the garden. What is the sum of all the numbers around the garden when all signs are in place?
Clues for the puzzle to solve; — means no number is given, not zero:
| Viewing side | Row/column 1 | Row/column 2 | Row/column 3 |
| --- | --- | --- | --- |
| Left (rows) | 3 | — | — |
| Right (rows) | — | 2 | — |
| Top (columns) | — | — | — |
| Bottom (columns) | 1 | — | — |