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^2-1)/(X-1) -1

By factoring X^2-1 into (X-1)(X+1), and dividing that by (X-1), 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

The number game you mentioned is a mathematical manipulation that exploits the properties of algebraic expressions to always yield a result of 1. Let's break down how it works using a specific example.

Let's say we choose the number 3. Applying the steps you mentioned:

1. Square the number: 3 * 3 = 9
2. Subtract one: 9 - 1 = 8
3. Divide by one less than the original number: 8 / (3 - 1) = 8 / 2 = 4
4. Subtract the original number: 4 - 3 = 1

No matter which number (except 1) you initially select, the end result will always be 1.

To further understand this process, let's rewrite the steps using a variable:

1. Start with a number, let's call it "x."
2. Square the number: x^2
3. Subtract one: x^2 - 1
4. Divide by one less than the original number: (x^2 - 1) / (x - 1)
5. Subtract the original number: [(x^2 - 1) / (x - 1)] - x

When we simplify this rational expression, we can see that it simplifies to 1, regardless of the specific value of x. This demonstrates the skill of simplifying rational expressions in algebra.

Now, let's create a new number game using the rules of algebra. Here's an example:

Take any algebraic expression (except one that results in division by zero). Square that expression and then subtract two. Divide by one less than the original expression. Now subtract your original expression. Did you reach 1 for an answer? You should have.

The goal of this new number game is to apply the same concept as before, but with algebraic expressions instead of specific numbers. Feel free to experiment with different expressions and discover the fascinating results!