Question 39
Denote by $d(A)$ the sum of all the elements of $A$ (if $A = \emptyset$, $d(A) = 0$). Let $S = \{1, 2, \dots, 2013\}$ and
$$
T_r = \{T \mid T \subseteq S, d(T) \equiv r \pmod 7\},
$$
for $r = 1, 2, \dots, 6$. Find the number of elements of $T_r$ for each $r$.
$$
T_r = \{T \mid T \subseteq S, d(T) \equiv r \pmod 7\},
$$
for $r = 1, 2, \dots, 6$. Find the number of elements of $T_r$ for each $r$.