MIP1502
ASSIGNMENT 3 (SEMESTER 0)..
DUE DATE: 18 JULY 2025..
PREVIEW:
QUESTION 1
COMPLETE TABLE
Diagram (n) 1 2 3 4 5 6 7 8 9 10
Small triangles 1 4 9 16 25 36 49 64 81 100
Black triangles 1 3 5 7 9 11 13 15 17 19
Grey triangles 0 1 3 6 10 15 21 28 36 45
White triangles 0 0 1 3 6 10 15 21 28 36
1.1.1 First differences and classification
1.1.1.1 First differences
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100):
First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19):
First differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Grey triangles (0, 1, 3, 6, 10, 15, 21, 28, 36, 45):
Disclaimer:
First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
The materials provided are intended for educational and informational purposes only. They should not be
submitted
White as original
triangles work
(0, 0, 1, 3, 6,or10,
used
15,in21,
violation
28, 36):of any academic institution's policies. The buyer is solely
responsible for how the materials are used.
First differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
,QUESTION 1
COMPLETE TABLE
Diagram (n) 1 2 3 4 5 6 7 8 9 10
Small triangles 1 4 9 16 25 36 49 64 81 100
Black triangles 1 3 5 7 9 11 13 15 17 19
Grey triangles 0 1 3 6 10 15 21 28 36 45
White triangles 0 0 1 3 6 10 15 21 28 36
1.1.1 First differences and classification
1.1.1.1 First differences
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100):
First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19):
First differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Grey triangles (0, 1, 3, 6, 10, 15, 21, 28, 36, 45):
First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
White triangles (0, 0, 1, 3, 6, 10, 15, 21, 28, 36):
First differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
1.1.1.2 Classification
• Small triangles: Quadratic (constant second differences)
• Black triangles: Linear (constant first differences)
• Grey triangles: Quadratic (constant second differences)
• White triangles: Quadratic (constant second differences)
, 1.1.1.3 Mathematical justification
The Black triangles are linear because their first differences remain constant at +2, showing
equal increase each time. The Small triangles are quadratic because their first differences
change at a constant rate (second differences always +2), indicating a squared growth
relationship.
1.1.2 Grey and White triangle patterns
1.1.2.1 Growth description
Grey triangles: The pattern grows by adding one extra triangle each time compared to the
previous increase, following the triangular number sequence.
White triangles: Growth starts from Diagram 3 onwards, with each diagram adding one
more triangle than the previous addition, mimicking Grey triangles but delayed by two
diagrams.
1.1.2.2 Flow diagrams
1.1.2.2 Flow diagrams
Grey triangles (n ≥ 1): White triangles (n ≥ 3):
Start
Start
Input (n)
Input (n)
Calculate total = n(n-1)/2
Calculate total = (n-1)(n-2)/2
Output total (number of Grey
triangles) Output total (number of White
triangles)
End
End
ASSIGNMENT 3 (SEMESTER 0)..
DUE DATE: 18 JULY 2025..
PREVIEW:
QUESTION 1
COMPLETE TABLE
Diagram (n) 1 2 3 4 5 6 7 8 9 10
Small triangles 1 4 9 16 25 36 49 64 81 100
Black triangles 1 3 5 7 9 11 13 15 17 19
Grey triangles 0 1 3 6 10 15 21 28 36 45
White triangles 0 0 1 3 6 10 15 21 28 36
1.1.1 First differences and classification
1.1.1.1 First differences
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100):
First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19):
First differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Grey triangles (0, 1, 3, 6, 10, 15, 21, 28, 36, 45):
Disclaimer:
First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
The materials provided are intended for educational and informational purposes only. They should not be
submitted
White as original
triangles work
(0, 0, 1, 3, 6,or10,
used
15,in21,
violation
28, 36):of any academic institution's policies. The buyer is solely
responsible for how the materials are used.
First differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
,QUESTION 1
COMPLETE TABLE
Diagram (n) 1 2 3 4 5 6 7 8 9 10
Small triangles 1 4 9 16 25 36 49 64 81 100
Black triangles 1 3 5 7 9 11 13 15 17 19
Grey triangles 0 1 3 6 10 15 21 28 36 45
White triangles 0 0 1 3 6 10 15 21 28 36
1.1.1 First differences and classification
1.1.1.1 First differences
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100):
First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19):
First differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Grey triangles (0, 1, 3, 6, 10, 15, 21, 28, 36, 45):
First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
White triangles (0, 0, 1, 3, 6, 10, 15, 21, 28, 36):
First differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
1.1.1.2 Classification
• Small triangles: Quadratic (constant second differences)
• Black triangles: Linear (constant first differences)
• Grey triangles: Quadratic (constant second differences)
• White triangles: Quadratic (constant second differences)
, 1.1.1.3 Mathematical justification
The Black triangles are linear because their first differences remain constant at +2, showing
equal increase each time. The Small triangles are quadratic because their first differences
change at a constant rate (second differences always +2), indicating a squared growth
relationship.
1.1.2 Grey and White triangle patterns
1.1.2.1 Growth description
Grey triangles: The pattern grows by adding one extra triangle each time compared to the
previous increase, following the triangular number sequence.
White triangles: Growth starts from Diagram 3 onwards, with each diagram adding one
more triangle than the previous addition, mimicking Grey triangles but delayed by two
diagrams.
1.1.2.2 Flow diagrams
1.1.2.2 Flow diagrams
Grey triangles (n ≥ 1): White triangles (n ≥ 3):
Start
Start
Input (n)
Input (n)
Calculate total = n(n-1)/2
Calculate total = (n-1)(n-2)/2
Output total (number of Grey
triangles) Output total (number of White
triangles)
End
End
