An open necklace can contain rubies, emeralds, and sapphires. At every step we can perform any of the following operations: We can replace two consecutive rubies with an emerald and a sapphire, where the emerald is on the left of the sapphire. We can replace three consecutive emeralds with a sapphire and a ruby, where the sapphire is on the left of the ruby. If we find two consecutive sapphires then we can remove them. If we find consecutively and in this order a ruby, an emerald, and a sapphire, then we can remove them. Furthermore we can also reverse all of the above operations. For example by reversing 3. we can put two consecutive sapphires on any position we wish. Initially the necklace has one sapphire (and no other precious stones). Decide, with proof, whether there is a finite sequence of steps such that at the end of this sequence the necklace contains one emerald (and no other precious stones). Remark: A necklace is open if its precious stones are on a line from left to right. We are not allowed to move a precious stone from the rightmost position to the leftmost as we would be able to do if the necklace was closed. Proposed by Demetres Christofides, Cyprus