128. Turn around matchsticks in a circle

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Place 7 sticks in a circle as shown with all heads pointing to the outside. The challenge is to turn around 6 of the 7 sticks with 6 heads pointing to the inside by following certain rules. The rules for turning a stick are:

1. Always start with a stick with head pointing to the outside.
2. You may go clockwise or anti-clockwise.
3. Start counting at a stick e.g. stick 3, skip stick 4 and turn around stick 5 so that the head now points to the inside.
4. Continue doing this until all the sticks, with the exception of one, point to the inside.

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One solution (going clockwise) would be:

Start at stick 2, skip 3 and turn 4.
Start at stick 7, skip 1 and turn 2
Start at stick 5, skip 6 and turn 7
Start at stick 3, skip 4 and turn 5
Start at stick 1, skip 2 and turn 3
Start at stick 6, skip 7 and turn 1

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