SOLUTION: A square checkerboard contains a rows and columns of squares. One checker piece is placed in each square on the boundary of the checkerboard. If b is the number of pieces required

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A square checkerboard contains a rows and columns of squares. One checker piece is placed in each square on the boundary of the checkerboard. If b is the number of pieces required       Log On


   

Question 973728: A square checkerboard contains a rows and columns of squares. One checker piece is placed in each square on the boundary of the checkerboard. If b is the number of pieces required to do this, what is one possible value of b?
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by josgarithmetic(39616) About Me  (Show Source):
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Draw a model if it helps. Top and bottom rows will have a and a pieces each. The remaining left and right columns have a-2 spaces each for containing pieces. The number of board pieces to fill the boundary spaces is then a%2Ba%2B%28a-2%29%2B%28a-2%29.

Simplified, 4a-4 boundary spaces for the checkerboard and you have 4a-4=b. You can find MANY possible values for b. One value which would not mean much is 0, which you'd have if a=1. No purpose in having such a checkerboard. Also, you cannot have a=0, because you cannot have meaning for b=-4. This value is nonsense. You must have a%3E1; in fact, that is also impractical. a=2? No. A board with only four spaces allows for insufficient movement of playing pieces.

The question is open-ended. Pick any value that makes sense for your purposes.