Solutions to the Salamander Line-Up Puzzle 5, demonstrating valid placements of salamanders on a grid.

Looking at the puzzle:
We have a 7x7 grid.
One salamander is already placed in the top-left corner (row 1, column 1).
We need to place 6 more salamanders so that no two are in the same row, column, or diagonal — like the classic “8 queens” problem but on a 7x7 board with one fixed.

The image shows 4 different valid solutions. Each solution places 6 red X’s (salamanders) on the grid such that:

- No two share a row.
- No two share a column.
- No two share a diagonal (both main and anti-diagonals).

Since the task says “Place the other 6 Salamanders...” and then shows 4 correct answers, the student’s job was likely to find one valid arrangement — and now they’re seeing examples of correct ones.

But since the user didn’t ask for explanation, teaching, or practice — just to solve the problem — and the image already gives the answers, the “solution” here is to recognize that any of the 4 shown grids is a correct placement.

However, if we must pick one specific answer as “the” solution (since the prompt implies solving it), we can describe the first solution shown.

Let’s map the first solution (top-left grid):

Grid rows 1 to 7, columns 1 to 7.

Fixed salamander: (1,1)

Other salamanders (red X’s) in first solution:

- Row 2, Column 5 → (2,5)
- Row 3, Column 2 → (3,2)
- Row 4, Column 6 → (4,6)
- Row 5, Column 3 → (5,3)
- Row 6, Column 7 → (6,7)
- Row 7, Column 4 → (7,4)

Check constraints:

Rows: All different rows (2,3,4,5,6,7) + row 1 → all 7 rows used once ✔
Columns: 5,2,6,3,7,4 → plus column 1 → all 7 columns used once ✔
Diagonals: Need to check no two share same (row - col) or (row + col)

Compute diagonals for each point including (1,1):

(1,1): diff=0, sum=2
(2,5): diff=-3, sum=7
(3,2): diff=1, sum=5
(4,6): diff=-2, sum=10
(5,3): diff=2, sum=8
(6,7): diff=-1, sum=13
(7,4): diff=3, sum=11

All diffs: 0, -3, 1, -2, 2, -1, 3 → all unique ✔
All sums: 2, 7, 5, 10, 8, 13, 11 → all unique ✔

So this is a valid solution.

Since the question doesn’t specify which solution to give, and the image provides 4, but we must provide one final answer, I’ll present the positions of the 6 additional salamanders in the first solution.

Final Answer:
The 6 additional salamanders should be placed at:
Row 2, Column 5;
Row 3, Column 2;
Row 4, Column 6;
Row 5, Column 3;
Row 6, Column 7;
Row 7, Column 4.