Computer With No Opening Book

Long ago, I had one of those early standalone chess computers -- "Chess Challenger," I think. Once you found a trap that it fell for, you could use it forevermore, and it would do exactly the same thing.

Once, I entered the standard starting position and presented it as a problem, asking the machine to make the best move given this position. This in effect stripped it of its stored opening "book" and forced it to rely upon the general idea of attacking the opposing king via gaining space and winning material. It was interesting how unusual an opening it played under these circumstances.

What about a modern 3000 rated program. Would it rediscover the popular openings by itself? Has anybody tried that?