Question 170
The Bank of Pittsburgh issues coins that have a heads side and a tails side. Vera has a row of $2023$ such coins alternately tails-up and heads-up, with the leftmost coin tails-up.
In a *move*, Vera may flip over one of the coins in the row, subject to the following rules:
* On the first move, Vera may flip over any of the $2023$ coins.
* On all subsequent moves, Vera may only flip over a coin adjacent to the coin she flipped on the previous move. (We do not consider a coin to be adjacent to itself.)
Determine the smallest possible number of moves Vera can make to reach a state in which every coin is heads-up.
In a *move*, Vera may flip over one of the coins in the row, subject to the following rules:
* On the first move, Vera may flip over any of the $2023$ coins.
* On all subsequent moves, Vera may only flip over a coin adjacent to the coin she flipped on the previous move. (We do not consider a coin to be adjacent to itself.)
Determine the smallest possible number of moves Vera can make to reach a state in which every coin is heads-up.