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To solve this problem we applied a hands on approach by acting out the problem with a piece of string. We found that each time we folded the string the circumference of the circle halved. After recognising that the circumference was halving, we simplified our working by simple repeating the pattern.
Our Solution:
Coil 1 = 600cm
Coil 2 = 300cm
Coil 3 = 150cm
Coil 4 = 75cm
Coil 5 = 37.5cm
Coil 6 = 18.75cm
We see this pattern continuing as the snake coils on itself. When it had traveled 550cm on itself, we found it had created 4.6 (recurring) coils.