Listen carefully and do this properly — no guesswork. I will show you a rigorous, step‑by‑step method that a top student must use, then give several fully checked candidate paths. If you want the final mark you must write coordinates clearly and verify each distance with the Pythagorean theorem.
1) Understand the moves (vector possibilities)
We start at (7,3). The sequence of move lengths is: 1, √10, 5, √5. Work with integer-coordinate differences (dx,dy) whose squares add to the required squared distance:
- Distance 1: dx^2+dy^2 = 1 → (±1,0) or (0,±1).
- Distance √10 (squared = 10): possible differences (±1,±3) or (±3,±1).
- Distance 5 (squared = 25): possible differences (±5,0),(0,±5),(±4,±3),(±3,±4).
- Distance √5 (squared = 5): possible differences (±1,±2) or (±2,±1).
Always check that each coordinate stays inside the 7×7 grid (x and y from 1 to 7). Also do not reuse a dot if the puzzle requires five distinct dots (the usual rule).
2) Do the systematic first step from the start (7,3)
Moves of length 1 from (7,3) give only three valid next points inside the grid:
- (6,3)
- (7,2)
- (7,4)
From each of these we compute every valid √10 move (differences (±1,±3) or (±3,±1)), then from each resulting point we compute every valid 5‑length move, and finally from each of those we compute the √5 finish options (differences (±1,±2) or (±2,±1)). You must check each step by calculating dx and dy and using dx^2+dy^2.
3) Three fully checked candidate solutions (all arithmetic verified)
I did the systematic search for you and validated the arithmetic. Each path below is a chain of 5 distinct lattice points with successive move lengths 1, √10, 5, √5. If the final dot must be one of the 12 marked dots on the Beast Academy diagram, check whether each point is marked — if it is, you have a valid puzzle solution.
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Path A (coordinates): (7,3) → (6,3) → (5,6) → (1,3) → (3,4)
- (7,3) to (6,3): dx = -1, dy = 0 → distance = √(1) = 1 ✔
- (6,3) to (5,6): dx = -1, dy = 3 → distance = √(1+9)=√10 ✔
- (5,6) to (1,3): dx = -4, dy = -3 → distance = √(16+9)=√25=5 ✔
- (1,3) to (3,4): dx = 2, dy = 1 → distance = √(4+1)=√5 ✔
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Path B (coordinates): (7,3) → (7,4) → (4,3) → (7,7) → (6,5)
- (7,3) to (7,4): dx = 0, dy = 1 → distance = 1 ✔
- (7,4) to (4,3): dx = -3, dy = -1 → distance = √(9+1)=√10 ✔
- (4,3) to (7,7): dx = 3, dy = 4 → distance = 5 ✔
- (7,7) to (6,5): dx = -1, dy = -2 → distance = √(1+4)=√5 ✔
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Path C (coordinates): (7,3) → (6,3) → (3,2) → (6,6) → (4,5)
- (7,3) to (6,3): dx = -1, dy = 0 → distance = 1 ✔
- (6,3) to (3,2): dx = -3, dy = -1 → distance = √10 ✔
- (3,2) to (6,6): dx = 3, dy = 4 → distance = 5 ✔
- (6,6) to (4,5): dx = -2, dy = -1 → distance = √5 ✔
All three are valid Pythagorean sequences on a 7×7 integer grid. Now: the Beast Academy puzzle requires you to pick 5 of the 12 marked dots. Without the diagram I cannot say which of the three completed paths uses only marked dots. You must check the diagram and see which of the coordinates above are marked. If at least one full path has all five points marked, that's your solution.
4) If none of those matches the 12 marked dots — what you must do next (strict checklist)
- Provide the Beast Academy diagram (photo or the list of the 12 marked coordinates). I cannot finish the final verification without it.
- If you want to find every possible candidate path yourself, systematically do this: from the start, list the three length‑1 neighbors; from each, list all valid √10 neighbors; from each of those, list all valid length‑5 neighbors; from each of those, list all valid √5 neighbors. Eliminate paths that use unmarked dots or repeat dots if repeats are not allowed.
- Always show your work: list the five coordinates and compute dx, dy and dx^2+dy^2 for each step. I will deduct points for sloppy or missing arithmetic.
5) Final instruction — deliverables for marking
Send me one of the following and I will mark it strictly:
- The Beast Academy diagram (photo) or a list of the 12 marked-dot coordinates — I will tell you which of the candidate paths above is valid, or I will find the correct path that uses marked dots.
- Or, if you checked the diagram yourself, send the path you claim is correct: list the five coordinates and show the four Pythagorean checks (dx,dy and dx^2+dy^2 for each step). I will grade it as exemplary only if the arithmetic is correct and the path uses only marked dots.
Do what I told you. If you post the marked-dot diagram now, I will finish the exact match and give you the ACARA‑aligned marking feedback.