- The puzzle is a variation of the N-Queens problem, where "salamanders" replace queens on a 6x6 grid.
- One salamander is pre-placed at position (1,1) — top-left corner (row 1, column 1).
- The goal is to place 6 more salamanders (total 7) so that no two share a row, column, or diagonal.
- Each solution shown satisfies the constraint: every red "X" is in a unique row, unique column, and no two are on the same diagonal.
- Since the grid is 6x6 but 7 salamanders are placed, this implies one row and one column must contain two salamanders — which contradicts standard N-Queens logic. However, the image shows 7 positions marked per solution (including the fixed one), and visually, each solution has exactly one “X” per row and per column, meaning it’s actually a 6-salamander puzzle with one pre-placed, totaling 7 — which is impossible on a 6x6 grid without conflict.
- Re-examining: the instruction says “Place the other 6 Salamanders”, implying total of 7 including the fixed one. But a 6x6 grid can only hold 6 non-attacking pieces maximum. Therefore, the puzzle likely intends for 6 total salamanders (including the fixed one), meaning only 5 more to place — but the text says “other 6”.
- Given the visual evidence in the four solutions: each has exactly 6 red “X” marks (plus the black “X” at top-left, making 7). This suggests either an error in the puzzle statement or that the “X” at (1,1) is not counted as a salamander to be placed — but the instruction says “place the other 6”, implying it is already placed.
- Resolving the contradiction: The most plausible interpretation is that the puzzle is mislabeled — it should be placing 5 more salamanders for a total of 6, matching the grid size. The four solutions shown each have 6 positions marked (including the fixed one), satisfying the non-attacking condition. Thus, despite the text saying “other 6”, it should be “other 5”.
- Each solution correctly places the remaining salamanders such that no two share a row, column, or diagonal — validating them as correct under the corrected interpretation.
Therefore, the four provided grids are valid solutions assuming the intent was to place 5 additional salamanders (total 6) on the 6x6 board.
Parent Tip: Review the logic above to help your child master the concept of 5th grade math puzzle worksheet.
