161854

Finding the solution was tricky so to help me I used a 600mm strip of paper (representing the 600cm snake) and marked every 50mm so I could see how far he had travelled. Then I could coil it around my hand to see how far he had to slither. On the first coil he had to travel 300cm, on the second coil he travelled an extra 100cm (the total distance travelled now 400cm). On the third coil he had to travel a difference of 50cm from the second coil (totalling 450cm), while for the fourth coil he had to travel a difference of 25cm from the third coil (now the total distance was 475cm). And for the fifth coil he had to travel a difference of 12.5cm from the fourth coil (new total is 487.5). I noticed that, not including the first coil, the difference between the distances he had to travel halves every time he goes round as 50 is half of 100, 25 is half of 50 and 12.5 is half of 25.