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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 ..."
Statement Snap
Age 7 to 14
Challenge Level 
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 ..."
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Prompt Cards
These two group activities use mathematical reasoning - one is numerical, one geometric.
Round and Round the Circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Gaxinta
A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?