Brain-Teaser 480

From The Sunday Times, 9th August 1970 [link]

The church hymn board shows the numbers of the four hymns chosen for the service. There are 800 hymns in the hymn book in use. The numbers are shown by slipping rectangular cards along the four grooved ledges.

Each card has a digit printed on each side of it, and there are no nines, inverted sixes being used instead.

What is the smallest number of cards which must be kept in stock so that the numbers of any four different hymns can be shown on the board?