Question 6
For each $1 \le i \le 9$ and $T \in \mathcal{N}$, define $d_i(T)$ to be the total number of times the digit $i$ appears when all the multiples of $2023$ between $1$ and $T$ inclusive are written out in base $10$. Show that there are infinitely many $T \in \mathcal{N}$ such that there are precisely two distinct values among $d_1(T), d_2(T), \dots, d_9(T)$.