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Prove that when a while square and a black square are
Chapter 8, Problem 46E(choose chapter or problem)
Prove that when a while square and a black square are removed from an 8 × 8 checkerboard (colored as in the text) you can tile the remaining squares of the checkerboard using dominoes. [Hint: Show that when one black and one white square are removed. each part of the partition of the remaining cells formed by inserting the barriers shown in the figure can be covered by dominoes.]
Questions & Answers
QUESTION:
Prove that when a while square and a black square are removed from an 8 × 8 checkerboard (colored as in the text) you can tile the remaining squares of the checkerboard using dominoes. [Hint: Show that when one black and one white square are removed. each part of the partition of the remaining cells formed by inserting the barriers shown in the figure can be covered by dominoes.]
ANSWER:SolutionStep 1In this problem, we have to prove that when one white and black square are removed from checkerboard we can tile the remaining square of the checkerboard using dominoes.Let us assume that a checkerboard will have 8 rows and 8 column. Here, in the beginning we have 32 white square and 32 black square.According to the given statement, if we remove one black and one white then the remaining white square will be 31 and black square is also 31 tiles.Now, According to the definition of Domino states that it is rectangle equal to the size of the two square either by parallel or perpendicular.