The letters L, M, N, O, P, Q, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?

We are given:
1. $P=4$
2. The difference between $P$ and $T$ is $5$, meaning $|P-T|=5$. Since $P=4$, $T$ can be $4+5=9$ or $4-5=-1$. Because the integers must be from $1$ to $9$, we must have $T=9$.
3. The difference between $N$ and $T$ is $3$, meaning $|N-T|=3$. Given $T=9$, $N$ can be $9-3=6$ or $9+3=12$. Since the integers must range from $1$ to $9$, we must have $N=6$.