Happy Birthday, Craig!

While hiking last weekend, I initiated a game. "Craig, I have the number 3888. You have 20 questions to figure out how I got that number." After a few questions and much deliberation, Craig learned that I multiplied 2 numbers together. He eventually arrived at 54x72. "So you just chose 2 random numbers and multiplied them?!" he asked in an exasperated tone.

"Yep! Now it's your turn."
After a long pause, Craig came up with his number. "One hundred sixty eight... THOUSAND... two hundred fifteen." At this point I was sure he didn't like my new game and was getting revenge on me with a huge, impossible number. I was determined, however. I asked a few questions and learned that he multiplied THREE numbers together: a one-digit number, a two-digit number, and a four-digit number. Through questioning I also determined that the two-digit number was between 10 and 20. Then I hiked silently while doing lots of division and multiplication. I figured out the answer. You have 20 questions to guess the 3 numbers.