Google announced the launch of a new Google-based trivia game for which it has partnered with the New York Times. It’s a daily puzzle called A Google A Day, where players are asked to use their “creativity and search skills on Google” to answer questions. It will appear above the crossword puzzle in the Times.

You don’t have to be a New York Times subscriber to play though. Google has set up a site for the game at agoogleaday.com, which features a game-specific version of the Google search engine, which players are supposed to use. It’s called Deja Google, which Google describes as “a wormhole inspired time machine that enables you to solve today’s puzzle spoiler free by searching the Internet as it existed before A Google a Day launched.”

This version of the search engine excludes real-time updates and other things that are “likely to include spoilers as people post the answers to the puzzle online.”

“As the world of information continues to explode, we hope A Google a Day triggers your imagination and helps you discover all the types of questions you can ask Google—and get an answer,” says Google user experience researcher Dan Russell.

There are actually questions from today, dating back to 04/07. You can look at past questions and answers, and share them with friends via Facebook, Twitter, Google Buzz, and email. You can also follow the questions via Facebook and Twitter.

Sounds like part of a “social layer” doesn’t it. Games are certainly a major part of social, and it will be interesting to see if Google continues to introduced fun little things like this, which could actually have a big impact in terms of user numbers.

It keeps users using Google to search too, even if it’s only “Deja Google”.