Question 7
Fede chooses $2008$ positive integers such that the product of these $2008$ numbers ends in $75$, and writes them on the blackboard. Then Iván, without seeing Fede's numbers, chooses a positive integer $k$ less than $2008$. If in Fede's list there are $k$ numbers whose product ends in $75$, Iván wins. Otherwise, Fede wins.
Determine all values of $k$ with which Iván is sure to win, no matter how well Fede plays.
Determine all values of $k$ with which Iván is sure to win, no matter how well Fede plays.