There are no three-digit numbers divisible by 6 that always leave a remainder of 1. This is because if a number is divisible by 6, it leaves a remainder of 0, not 1.
Explanation:
A number divisible by 6 can be written as 6n, where n is an integer. By definition, 6n leaves a remainder of 0 when divided by 6. Therefore, it is impossible for a number divisible by 6 to simultaneously leave a remainder of 1. The statement is contradictory.
