we want to tile a 2 x n strip with 2x2 square tiles that are yellow and green, 2x2 L shaped tiles that are blue and red and 1 x 1 orange tiles give a formula for the number T(base n) of such tilings. Your solution must consist of a recurrence equation for T(base n) with a complete justification, followed by a solution of this recurrence.
we want to tile a 2 x n strip with 2x2 square tiles that are yellow and green, 2x2 L shaped tiles that are blue and red and 1 x 1 orange tiles give a formula for the number T(base n) of such tilings. Your solution must consist of a recurrence equation for T(base n) with a complete justification, followed by a solution of this recurrence.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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we want to tile a 2 x n strip with 2x2 square tiles that are yellow and green, 2x2 L shaped tiles that are blue and red and 1 x 1 orange tiles
give a formula for the number T(base n) of such tilings. Your solution must consist of a recurrence equation for T(base n) with a complete justification, followed by a solution of this recurrence.
Transcribed Image Text:**Available Tiles:**
The image showcases five distinct types of tiles. Each tile varies in shape and color:
1. A yellow square tile.
2. A green square tile.
3. A larger blue L-shaped tile.
4. A red L-shaped tile.
5. A small orange square tile.
**Example of a 2 x 12 Strip Tiling:**
Below the available tiles is an example of how these tiles can be arranged to fill a strip measuring 2 units in height and 12 units in length. The tiling is organized as follows:
1. A red L-shaped tile is placed on the far left.
2. Following it is a blue L-shaped tile.
3. Next, a yellow square tile is positioned.
4. A green square tile follows.
5. The small orange square tile is placed in the fifth position.
6. Finally, the strip is completed with two blue L-shaped tiles.
This example demonstrates how diverse tile shapes can be combined to fill a given area.
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