Sunday Times Teaser 2542 – Two Routes
by Graham Smithers
Published: 12 June 2011 (link)
A line of equally spaced poles is marked in order with odd numbers, 1, 3, 5, etc. Directly opposite is a parallel line of an equal number of poles with even numbers, 2, 4, 6, etc. There are fewer than 100 poles. The distance in metres between adjacent poles is a two-digit prime; the distance between opposite poles is another two-digit prime. Jan walks the route 1-2-4-3-5, etc to reach the final pole. John walks the odds 1-3-5, etc to the last odd-numbered pole; then walks diagonally to pole 2; then walks the evens 2-4-6, etc, also finishing at the final pole. Jan’s and John’s routes are of equal length.
How many poles are there?