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Problem 3: We want to tile an n × 1 strip with 1 × 1 tiles that are green (G), blue (B), and red (R), 2 × 1 purple (P) and 2 × 1 orange (O) tiles. Blue cannot be next to purple tile, and there should be no two purple or three blue tiles in a row (for ex., BBOORGP is allowed, but BBBOGR, PBOGP and OPPRO are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.

Problem 3: We want to tile an n × 1 strip with 1 × 1 tiles that are green (G), blue (B), and red (R), 2 × 1 purple (P) and 2 × 1 orange (O) tiles. Blue cannot be next to purple tile, and there should be no two purple or three blue tiles in a row (for ex., BBOORGP is allowed, but BBBOGR, PBOGP and OPPRO are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Problem 3: We want to tile an n × 1 strip with 1 x 1 tiles that are green (G), blue (B), and red (R), 2 × 1 purple (P) and 2 × 1 orange (O) tiles. Blue cannot be next to purple tile, and there should be no two purple or three blue tiles in a row (for ex., BBOORGP is allowed, but BBBOGR, PBOGP and OPPRO are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.
Transcribed Image Text:Problem 3: We want to tile an n × 1 strip with 1 x 1 tiles that are green (G), blue (B), and red (R), 2 × 1 purple (P) and 2 × 1 orange (O) tiles. Blue cannot be next to purple tile, and there should be no two purple or three blue tiles in a row (for ex., BBOORGP is allowed, but BBBOGR, PBOGP and OPPRO are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.
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