MIP1502 ASSIGNMENT 4 2024 solution

Assignment 4: Compulsory
Contributes 25% to the final pass mark
Unique number: 397869
Due date: 16 August 2024

, Question 1


1.1.1


Tile number (n) 5 6

Tile length (l) 7 8

Number of red squares (𝑅) 12 14


Number of black squares 37 50
(𝐵)
Total number of squares 49 64
(𝑆)


1.1.2


 The pattern shows that the total number of squares (S) for any tile number (n) is equal
to the square of the tile length (l).
 Therefore, the tile length (l) increases by 1 as the tile number (n) increases by 1.
 So, for tile number 7:
 l=n+2=7+2=9


1.1.3.1

 Rn = 2n + 2 where n is the tile number.

Given l = n + 2, it can be rewritten as Rn in terms of l:

R = 2 (L−2) + 2 = 2L−4.

1.1.3.2
Given that the sequence of black squares follows a quadratic pattern,