If today is Sunday, what day is 10 ^ 99 days later? The answer is Sunday, Quick algorithm without calculator

If today is Sunday, what day is 10 ^ 99 days later? The answer is Sunday, Quick algorithm without calculator

The remainder is 6, because the decimal of 1 / 7 circulates according to 142857. The corresponding remainder of 10, 100, 1000, 10000, 100000 and 1000000 divided by 7 is 3, 2, 6, 4, 5 and 1, that is, every 10 ^ 6, the remainder circulates. 99 divided by 6, the remainder is 3, and the corresponding remainder divided by 7 should be the third one listed above, which is 6