Problem of the Week 1215

Connect the Dots

Consider a 5 × 5 square lattice of 25 points. Find the longest path (in terms of number of segments) that:

• connects lattice points in sequence with straight segments and never intersects itself (even a tangency is not allowed); and
• has each segment of strictly greater length than the segment that precedes it

For example, on a 3 × 3 lattice, the longest such path has length 4: it is

(0, 0) → (0, 1) → (1, 2) → (1, 0) → (2, 2)

Source: Oct 2014 Crux Math, p. 318, originator is Gordon Hamilton.

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