Pow 3 Rectangles

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Problem statement:

What you are trying to find is how many rebounds and in what corner will a pool ball land. Each shot will start at the lower left corners and will always start moving at a 45 degree angle. The table is a rectangle with pockets in each of the four corners.The pool table has whole number dimensions. I am trying to figure out the patterns or formulas for the pool table.


I first started making squares and rectangles on a graph paper, and did this in a group of three. Then I started drawing lines at a 45 degree angle, if they hit one of the sides of the wall then I would keep on drawing the lines at a 45 degree angle until the ball would go into one of the pockets. If you wouldn’t keep on drawing lines until …show more content…

But the one thing that I didn’t quite get to is the super solution but all of my mini solutions work for all sorts of rectangles. My solutions were two of the same numbers always equal zero. I know that this works because if you do a 6 by 6 you would get 0 rebounds. A number and one are always the number subtracted by one. If you do a 4 by 1 you would get 3 rebounds. If the dimensions can be reduced to ½ then the rebound will be one. For example, an 8 by 4 has one rebound. If the dimensions have a two in it, then the other number is the number of rebounds that you have. For example, If you had a 7 by 2 there would be 7 rebounds. You take the first dimension and add it to the second dimension and subtract it by 2. This one works for most of them but not all of them. For example, if you had a 9 by 7 then there would be 14 rebounds. The ball never lands in the corner, it was shot from. I looked at all the pictures that I drew to figure out the formulas and noticed that the corner the ball was hit from, never ever landed in the corner that it was hit from. Finally, if there are 0 rebounds then the ball will land in the corner diagonal from the corner it was shot. I figured this out by looking at the rebounds and pictures that I drew for the 0 rebounds. Those were all of the formulas and patterns that I found. This is a one by one which has 0

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