\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16\n* * * * * * * * * * * * * * * *\n* 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16\n* 2 3 4 * * * 8 9 10 * * * 14 15 16\n* 2 3 * * * * * 9 10 * 12 * 14 15 *\n* 2 3 * 5 * * * 9 * * 12 * 14 * *\n* 2 3 * 5 6 * * 9 * * * * 14 * *\n* 2 3 * 5 6 7 * 9 * * * * * * *\n* 2 3 * 5 6 7 8 9 * * * * * * 16\n* 2 3 * 5 6 7 8 * 10 11 12 13 14 15 *\n
Start with N cards with the number N on the face, in order, face up.
Turn over every card.
Turn over every other card.
Turn over every third card.
Etc. until you reach N div 2 + 1 (integer division). Turn over that one and all the others to the right, and you're done.
Explain why some cards are left face down :)