About 10 years ago, when I was still in high-school, I took a science fiction course. In that course we used an anthology book from the 1960's, which contained stories from the 1930's until the time of publishing.
One of the stories was about a man, who was in some sort of military unit. He was separated from that unit, and left alone on some alien landscape. At some point he discovers an energy barrier of some sort. Across this barrier, he sees his mortal enemy - an alien described as being an organic wheel. The story involves them trying to cross the barrier to fight each-other.
Clarified, courtesy of SQB
They both try crossing the barrier, but it seems only non-living objects can cross it. They both construct catapult-like machines to shoot at each other. Then the human discovers unconscious objects can cross as well. So he knocks himself out just right to fall through and beats the alien. He is then transported back to his unit by the godlike entity that brought them there to determine the future of their races. Since the human soldier won, humans have won as well. Unfortunately, I don't recall the name nor the author
Other stories from this anthology include one about a doctor's bag from the future being sent back in time to 'the present', and an Arther C. Clark (I think) story about a computer being used to compute the names of God in a Buddhist temple.
Ideally, I would like to know the name of the anthology (preferably with an ISBN), but I would really like to know the name of the first short story I described, and the name of it's author.