We need to minimise our answer for each possibility.
There 60 cross-headed screws whilst the other 40 are slot headed.
70 of the screws are 3mm in diameter. In order to minimise this figure, we need to assume that all 40 slot headed screws are 3mm in diameter which leaves us with 30 cross-headed screws with 3mm diameter.
The other criteria is length of screws. We have 80 screws that are 50mm long, 20 which are not 50mm long. We need to assume that the 20 which are not 50mm long are all cross headed.
Therefore, we have 30-20 = 10
The smallest number of cross-headed, 3mm diameter and 50 mm long are 10.