matches: correct is six

(easy to draw, but very difficult to describe: the first three in form of an arrow with the shaft a bit behind so that the two outer matches meet slightly in front of the shaft match which they also both touch; the next three in the identical formation but laying just above the first three but the direction of the arrow is perpendicular to the first arrow)

cigarettes: seven is correct

of course, the same solution as with the matches also works, but there is an ingenious solution with seven which doesn't work with the matches (depends upon the relation between length and width). This solution is so complicated that I think I can't describe it sufficiently, but I'll try: You start with a cigarette standing up. The next three cigarettes are placed around the first cigarette in a way that each butt touches the first cigarette and the butts form a tiny triangle with equal sides just around the butt of the standing up cigarette. It kind of looks like a three blade wind rotor. The last three cigarettes are placed one storey up in the same way as the other three cigarettes but in a slightly different angle so they are supported by each of the three basement cigarettes at one point. Very difficult to do actually, but it is theoretically possible and that's all that is needed in mathematics.

Wolfgang