Find the remainder when the number 12121212… (100 digits) is divided by 1001

The number is (12 * 10^98) + (12 * 10^96) + ... + 12. This is a geometric series. 1001 = 7 * 11 * 13. Using modular arithmetic, 10^3 = -1 mod 1001. The pattern repeats every 6 digits (121212). 100 digits / 6 = 16 groups of 121212 plus 4 digits (1212). 1212 mod 1001 = 211. This is not the standard approach, but calculation confirms 666.