09 June 2011

45. Turn matchsticks in the circle

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In the layout above 8 matchstick heads are pointing to the OUTSIDE. The challenge is to turn 7 of the 8 matchsticks so that the heads are pointing to the INSIDE. The following rules apply when turning matchsticks:

1. Start every time on a matchstick with head pointing to the OUTSIDE.
2. Skip 3 matchsticks (INCLUDING the one you started on) and turn the 4th matchstick with head pointing to the INSIDE.
3. You may only move CLOCKWISE.

For example, start on matchstick number 7, count clockwise, 7, 8, 1 and turn stick no 2. Another example would be to start on number 5, count 5, 6, 7 and turn number 8.

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One solution is:

8,1,2 turn 3
5,6,7 turn 8
2,3,4 turn 5
7,8,1 turn 2
4,5,6 turn 7
1,2,3 turn 4
6,7,8 turn 1

A general solution would be to turn the matchstick on which you started the previous round. Look at the solutions above. If you turn number 7, you should have started on 7 the previous round.

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