10-1-1. Select the numbers that serve as counterexamples to the given statement: “If the sum of the digits of a natural number is divisible by 27, then the number itself is divisible by $27$.”

a) 81 ; b) 999 ; c) 9918 ; d) 18 .
Answer: only 9918.

Solution option 1. The statements about 81 and 18 are definitely not counterexamples, as for them, the premise "if the sum of the digits of a natural number is divisible by 27" is not satisfied.

The statement about 999 is not a counterexample, as it does not contradict our statement.

Finally, the number 9918 is a counterexample, since for it, the sum of the digits is divisible by 27, but the number itself $9918=9 \cdot 1102$ is not divisible by 27.