Question

(Difficulty: 4/10)

What is the remainder of 1111....1 (a total of 2017 '1' s) divided by 12?

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Solution

A number is divisible by 12 if it is divisible by 3 and 4.
Method of checking if a number is divisible by 3: Sum up all its digits and see if it is divisible by 3.
Method of checking if a number is divisible by 4: See if the number formed by the last 2 digits are divisible by 4.
Therefore, the closest number is 111...1116.
Because the sum of digits is 2022, which is divisible by 3; and its final 2 digits is 16, which is divisible by 4.
Therefore the remainder is 7.