The hamsters wanted some fruit and ate the post. It’s not only squirrels liking the seeds.
I’ll work from the title.
Two nice big pictures for those like me who have never seen it before.
http://www.mcmullans.org/canal/osage_orange.htm
http://members.iglou.com/perkins/newkpf/2001_11/home3507.htm
It’s an aggregate fruit, made from smaller parts that grew together. Here’s a page with a picture of its flowers: http://www.extension.iastate.edu/pages/tree/osage-or.html
http://waynesword.palomar.edu/jackfr1.htm
and further down http://waynesword.palomar.edu/jackfr1.htm#osage