movies they were putting on 4 shelves. If the owner wanted to make sure each shelf had the same number of movies, how many more movies would he need?

Let’s say the owner currently has a total of \(N\) movies. To put an equal number of movies on 4 shelves, the total number must be divisible by 4. In other words, \(N\) must be a multiple of 4. If \(N\) when divided by 4 leaves a remainder, we can write \[ N = 4q + r, \] where \(q\) is the quotient and \(r\) (with \(0 \le r < 4\)) is the remainder. To have exactly 4 equal groups the owner needs the next multiple of 4. The next multiple is \[ 4(q+1) = 4q + 4. \] The number of additional movies needed is the difference: \[ \text{Additional movies} = 4(q+1) - N. \] Since \(N = 4q + r\), this difference becomes \[ 4(q+1) - (4q + r) = 4 - r. \] Thus, the owner needs \[ \boxed{4 - r} \] more movies, where \(r\) is the remainder when \(N\) is divided by 4. Equivalently, if you compute \[ r = N \mod 4, \] then the required additional movies is \[ 4 - (N \mod 4) \] (choosing \(0\) if \(N \mod 4=0\)).