We have a set of N coins that are all placed in a circle. They all have "Tails" as their face up side. The coins are all distinct and have numbers (1,2,3...N) written on them.
In each move, we flip any 3 consecutive coins. That is, consider:
H H H T T
If I decide to flip the coins 3,4 and 5 then I will get : H H T H H
Now, there can be 2^N distinct heads-tails permutations of N distinct coins.
1.Prove/disprove that there is a finite set of moves in which we can reach any one of the (2^N) heads-tails permutation of these N coins, from the initial all tails permutation.
2.Also, if reaching any permutation is indeed possible, then what is the maximum number of moves that are needed to get to any permutation from the initial all tails permutation.
For further clarification,if N was 3, for example, then the 2^3 distinct permutations of these 3 coins would be: