I came across this twist on the Mobius Strip today and it is too good not to share. It is from Martin Gardener whose birthday is today (21st October).
First, cut two strips of paper:
Then tape them in the shape of a cross:
Now tape them so that you create one Mobius strip and one normal loop:
Now trisect the Mobius strip part and bisect the normal loop part.
But before you do, predict what will happen.