Challenge Level

Imagine a $600$ cm snake that coils into a circle, but he's not going to eat himself.

**Challenge **
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Final challenge

When the snake has slithered a total of $550$cm along his body length, making smaller and smaller circles of his body, how many circles will there be?

He is going to coil himself around to make a double circle, then a treble circle and so on until he is coiled round like this rope.

Once in a circle how much further will he have to slither to make a double circle of his body? What's this length as a fraction of his total length?

How much further will he have to slither to make three circles of his body?

What's this length as a fraction of his total length?

How much further will he have to slither to make four circles of his body?

What's this length as a fraction of his total length?

How much further will he have to slither to make five circles of his body?

What's this further length as a fraction of his total length?

Final challenge

When the snake has slithered a total of $550$cm along his body length, making smaller and smaller circles of his body, how many circles will there be?