Longest Road

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Gordon Hamilton · Longest Road: A Spatial Reasoning Puzzle

Longest Road is played on a board of points joined by lines. The board marks a starting point. Find the point that is furthest from it, where distance is not measured as the crow flies but as the number of steps you must travel along the lines to get there. The answer is the point at the greatest number of steps, and the puzzle is to find it by reasoning rather than by guessing.

The idea is spatial. A point can look far away on the page and be close along the lines, or look close and be a long walk away. To find the furthest point, players trace routes through the maze, compare candidates, and test the best one by counting. When a guess is wrong, the count shows how far off it was, and that narrows the search. Players learn to check several candidates before committing, and to treat a long count as evidence rather than a feeling. Once the board is familiar, the puzzle can become a timed challenge, where speed comes from recognising the shape of the maze.

In the classroom, start on a small board so the class can count every route together. Then move to a larger board, and let pairs compare their answers and argue over which point really is furthest.

Grades
1–6
Subjects
Counting & Estimating, Logic
Kind
Game

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