Answer: What if you used one big pen containing
three little pens. It's easy to distribute the animals then -- say,
7, 7, and 13. Each small pen contains an odd number, and the big
pen contains all twenty-seven, also an odd number. Another even simpler
solution puts the animals inside a pen inside a pen inside a pen inside
a pen. This solution fits the stipulations of the problem, but it
seems less plausible than one pen containing three pens.