What animal eats tulip petals at night?

Okay, this is very strange. Our tulips just bloomed this past week and 4 of the 5 where gone yesterday morning. The petals at the top of the stem looked like it was sheared off. The leaves and stem left intact. Then the 5th tulip was gone this morning! What night critter would do something like this? A few of the petals I found on the ground just inches away. Our neighborhood has squirrels (didn't think they were nocturnal) and rabbits occasionally - although the head of the tulip is at least 14-16" off the ground.