You might like to take a look at the problem Satisfying Statements together with the accompanying Teachers' Resources, as the game and the problem have been designed to complement one another.
You may wish to start your students off with the simplest scoring system, so that they can get used to the game, and then move on to the more challenging versions which might pique students' curiosity and generate interesting insights and discussions:
"If I know that 49 is a square number and a multiple of 7, then I know that 4900 is as well. Or 490000. Or 49000000..."
"If I know that 18, 38, 58, 78 and 98 are even but not multiples of 4, and 2 less than a multiple of 10, then so are 118, 138, 158, 178 and 198. Or 218, 238, 258, 278 and 298, or ..."