Suppose you have a ring of circles. A circle has two states: on (yellow) and off (black). It starts with all circles being off. A move consists of picking a circle, and switching its state together with the states of the two neighboring circles (we assume there are at least 3 circles). The initial configuration is all circles being off.
Question: suppose you have 17 circles. Are all configurations reachable in a set of moves? If not, which ones are reachable? Next, do the same for 18, 19 and 20 circles.
The case of 5 circles is illustrated in the diagram.
If you have figured out the answer, please don't spoil it to others. In fact, better not post the answer at all, just tell us how you liked the puzzle. If there is demand I will post the answers in the second thread.
Question: suppose you have 17 circles. Are all configurations reachable in a set of moves? If not, which ones are reachable? Next, do the same for 18, 19 and 20 circles.
The case of 5 circles is illustrated in the diagram.
If you have figured out the answer, please don't spoil it to others. In fact, better not post the answer at all, just tell us how you liked the puzzle. If there is demand I will post the answers in the second thread.
