This is a beautiful puzzle that appears in many different forms.
Arp and Bif are playing with a line of 100 flowers. Each flower is originally open. When an open flower is touched it closes, and when a closed flower is touched, it opens. First they touch every flower in the line, then they touch every other flower in the line, then they touch every third flower, etc.
When done, which flowers are open, which flowers are closed?