\section*{Problem 5}

Does there exist a 4-digit integer which cannot be changed into a multiple of 1992 by changing 3 of its digits?

\section*{Answer \(\quad\) Yes, eg 2251}


\section*{Solution}

The only 4 digit multiples of 1992 are: 1992, 3984, 5976, 7968, 9960. All have first digit odd, second digit 9 , third digit \(>5\) and last digit even, so it is easy to find a number which has all digits different from all of them.

