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

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) (Show Source): You can put this solution on YOUR website!
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Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
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 .

Simplified, boundary spaces for the checkerboard and you have . 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 ; in fact, that is also impractical. ? 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.
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