I loved this puzzle so much that I ended up putting the original picture for the puzzle, not realising that the one Martin Gardner had put in his book was a different one, and therefore some of the description of the puzzle was not matching the picture, as pointed out by Suman Saraf – thanks Suman! Anyway, the puzzle still was a valid one. I only received two correct solutions – Suman Saraf and from my niece, Radhika Goyal. Well done both!
It was not an easy puzzle. The trick, at least for me, was to try it both backwards and forwards and find a meeting path. Here is a solution to the puzzle:
It might be easier to see the video as the answer, link attached here:
Hope you all enjoyed the puzzle!