Question 64
Thanima owns a magnificent necklace made of rubies, emeralds and sapphires, which we represent by a sequence of $R$, $E$ and $S$. In one magic operation, she can perform one of the following actions:
- Replace a pattern $RR$ in the necklace by a pattern $ES$ (or $ES$ by $RR$).
- Replace a pattern $EEE$ by a pattern $SR$ (or $SR$ by $EEE$).
- Delete a pattern $SS$, or add a pattern $SS$ anywhere.
- Delete a pattern $RES$, or add a pattern $RES$ anywhere.
It is not possible to shift the letters cyclically because of the clasp. Nor can she turn the necklace over.
Is it possible to go from a necklace containing only one sapphire to a necklace containing only one emerald by magic operations?
- Replace a pattern $RR$ in the necklace by a pattern $ES$ (or $ES$ by $RR$).
- Replace a pattern $EEE$ by a pattern $SR$ (or $SR$ by $EEE$).
- Delete a pattern $SS$, or add a pattern $SS$ anywhere.
- Delete a pattern $RES$, or add a pattern $RES$ anywhere.
It is not possible to shift the letters cyclically because of the clasp. Nor can she turn the necklace over.
Is it possible to go from a necklace containing only one sapphire to a necklace containing only one emerald by magic operations?