Question 157
Rthea, a distant planet, is home to creatures whose DNA consists of two (distinguishable) strands of bases with a fixed orientation. Each base is one of the letters $H$, $M$, $N$, $T$, and each strand consists of a sequence of five bases, thus forming five pairs. Due to the chemical properties of the bases, each pair must consist of distinct bases. Also, the bases $H$ and $M$ cannot appear next to each other on the same strand; the same is true for $N$ and $T$. How many possible DNA sequences are there on Rthea?