Algebra
posted by Noah .
I just need help with the number game part. I can't think of any kinds of games to come up with?
Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reached 1 for an answer? You should have. How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra.

If X is the number you select, your operations result in
(X^21)/(X1) 1
By factoring X^21 into (X1)(X+1), and dividing that by (X1), you should be able to see why your number game works  except when X = 1.
Make up your own game using rules of algebra. This should show you how to do it. 
trying to create a nimber game