Question 49
There are $2014$ coins each of which is black on one side and white on the other side. A $2014 \times 1$ board is given. One coin is placed on each square. In each move we can remove one coin with black side up and, at the same time, flip the coins on the neighbouring squares (if they were not already removed).
Determine all starting arrangements of coins such that there is a finite sequence of moves which removes all the coins. (New Zealand)
Determine all starting arrangements of coins such that there is a finite sequence of moves which removes all the coins. (New Zealand)