Circles & Lines · Hard problem

A four-digit positive integer has digits $d_1, d_2, d_3, d_4$ (read left to right) that form an arithmetic progression with common difference $2$, so $d_2 = d_1+2$, $d_3=d_1+4$, and $d_4=d_1+6$, with $d_1 \ge 1$. How many such four-digit integers are divisible by $11$?