Question 3
A 4035-digit number is a multiple of 13. Its first 2017 digits are all 5s, and its last 2017 digits are all 6s. What is the middle digit?
$$\underbrace{555\cdots55}_{2017\ \text{digits}}\ ?\ \underbrace{666\cdots66}_{2017\ \text{digits}}$$
$$\underbrace{555\cdots55}_{2017\ \text{digits}}\ ?\ \underbrace{666\cdots66}_{2017\ \text{digits}}$$