Buzz Lightyear - Wet or Dry

How the heck do you train a 3 year old to get up at night to go to the bathroom? I opted for bribery. I told Reilly that if his pull-up was dry in the morning he could get a new puzzle. The morning after the bribe - although I distinctly smelled the strong odor of urine - I asked

Is your pull-up dry?

No, but I was going to put on a new one - then it would be dry - then I can get a puzzle.

Ahhhh, I'm confused. How does this work again? And can I have a child that is THAT clever at 3 years old?