nicetry007 wrote: The multiples of 1992 less than 10000 are as follows:$ \{1992, 3984, 5976, 7968, 9960\}$. Essentially, we need to find a 4 digit number whose leading digit differs from the leading digit of all the multiples, whose second digit differs from the second digit of all the multiples and so on. The $ i$-th set in the following collection of sets is the set of feasible digits for the $ i$-th position. $ \{ \{2,4,6,8\}, \;\{0,1,2,3,4,5,6,7,8\}, \;\{0,1,2,3,4,5\}, \;\{1,3,5,7,9\}\}$. The smallest number satisfying the property is 2001 and there are $ 4 \cdot 9 \cdot 6 \cdot 5 = 1080$ numbers with the required property.

There is no stated requirement that, after the replacement, the resulting number must still be a $4$-digit integer. This being said, if we replace in $2001$ the first and last digits with $0$, we get $0$ (a quite valid number, I'd say), which is a multiple of $1992$. So either add that requirement to the statement, or remove the $0$'s from those lists. Anyways, $2111$ always works.