Nicely warm and curious — let us slice this puzzle like a fine tart: use the Pythagorean theorem to compute straight-line distances between the marked grid points, then arrange the points so the consecutive distances equal 1, √10, 5, √5.
- List the marked points (from the puzzle): A = (5,0), B = (6,3), C = (1,3), D = (6,2), E = (3,2).
- Recall: distance between (x1,y1) and (x2,y2) is sqrt((x2−x1)^2 + (y2−y1)^2). We will compute useful pairwise distances.
- Compute the key distances (showing dx, dy):
- D(6,2) to B(6,3): dx = 0, dy = 1 → distance = sqrt(0^2 + 1^2) = 1.
- B(6,3) to A(5,0): dx = -1, dy = -3 → distance = sqrt(1 + 9) = sqrt(10).
- A(5,0) to C(1,3): dx = -4, dy = 3 → distance = sqrt(16 + 9) = sqrt(25) = 5.
- C(1,3) to E(3,2): dx = 2, dy = -1 → distance = sqrt(4 + 1) = sqrt(5).
- Strategy: find the unique pair at distance 1 to anchor the sequence. Only D–B = 1, so the sequence must pass through D and B consecutively. Try ordering so the next distances match √10, 5, √5.
- Following that anchor, choose B → A (distance √10), then A → C (distance 5), then C → E (distance √5). This uses all five points once and gives the required consecutive distances.
- Final continuous path (in order): D(6,2) → B(6,3) → A(5,0) → C(1,3) → E(3,2). Distances: 1, √10, 5, √5 — verified above.
Tip: when puzzles ask for a sequence of specific lengths, compute pairwise distances first, mark unique matches (like the single length of 1), and build outward. That way you taste the solution step by step, like seasoning to perfection.
50-word ACARA v9-aligned teacher comment (Nigella cadence):
Sumptuous reasoning: the student skilfully applies Pythagoras to compute lengths, selects and sequences coordinates accurately, and verifies each step. Clear diagrams, precise calculations and logical justification show mastery. Minor arithmetic slips are addressed. Assessment aligns with ACARA v9: problem-solving, reasoning, communication and correct application of geometric concepts and accuracy celebrated.
Well done — the path is found and each step checked. If you want, I can draw the 7×7 grid with the path marked or show the same reasoning with a diagrammatic animation.