Mathematical Structures - Assignment 2004 | MAT 300, Assignments of Mathematics

Material Type: Assignment; Class: Mathematical Structures; Subject: Mathematics; University: Arizona State University - Tempe; Term: Spring 2004;

Typology: Assignments

Pre 2010

Uploaded on 09/02/2009

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In Class Activity
MAT 300, Spring 2004
March 23, 2004
Tiling a Checkerboard
1. Consider a standard checker board (red and black alternating squares, 8 x 8). Can
you cover the entire board with dominos, without any domino overlapping?
2. What if one black square and one red square were removed from the corners of the
board? Can you cover the entire board with non-overlapping dominos?
3. Now cover any one red square and any one black square with a single square tile on
each. Is it possible to cover the remaining portion of the board with dominos? Justify
your answer.
4. Can you prove this is the case for the remainder of any checker board (alternating red
and black squares) of dimension 2n x 2n after one black and one red square have been
covered? Justify your answer.
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In Class Activity MAT 300, Spring 2004 March 23, 2004

Tiling a Checkerboard

  1. Consider a standard checker board (red and black alternating squares, 8 x 8). Can you cover the entire board with dominos, without any domino overlapping?
  2. What if one black square and one red square were removed from the corners of the board? Can you cover the entire board with non-overlapping dominos?
  3. Now cover any one red square and any one black square with a single square tile on each. Is it possible to cover the remaining portion of the board with dominos? Justify your answer.
  4. Can you prove this is the case for the remainder of any checker board (alternating red and black squares) of dimension 2n x 2n after one black and one red square have been covered? Justify your answer.

An L-Tiling of the Checkerboard

  1. Consider an 8 x 8 board. Place a single square tile on one square from the board. Is it possible to cover the remaining board with non-overlapping L-shaped pieces?
  2. Can you prove this is the case for any board with dimensions 2n^ x 2n^ and one square covered? Justify your answer.
  3. What can you say if the board does not have dimensions 2n^ x 2n? Justify your answer.