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 Analysis of Patterns
1.1.1.1 First differences (1)
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
Differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19)
Differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Disclaimer:
Grey trianglesprovided
The materials (0, 1, 3,are
6, 10, 15, 21,
intended for28, 36, 45) and informational purposes only. They should not be
educational
Differences:
submitted as 1, 2, 3, 4,
original 5, 6,
work or7, 8, 9in violation of any academic institution's policies. The buyer is solely
used
responsible for how the materials are used.
White triangles (0, 0, 1, 3, 6, 10, 15, 21, 28, 36)
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 Analysis of Patterns
1.1.1.1 First differences (1)
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
Differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19)
Differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Grey triangles (0, 1, 3, 6, 10, 15, 21, 28, 36, 45)
Differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
White triangles (0, 0, 1, 3, 6, 10, 15, 21, 28, 36)
Differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
1.1.1.2 Classification
• Small triangles: Quadratic (second differences constant)
• Black triangles: Linear (first differences constant)
• Grey triangles: Quadratic (second differences constant)
• White triangles: Quadratic (second differences constant)
, 1.1.1.3 Justification
The Black triangles pattern has a constant first difference (2), indicating a linear sequence
where each term increases by the same amount. The Small triangles pattern has first
differences (3,5,7,9...) that themselves increase consistently, indicating a quadratic sequence
because the second difference is constant (always 2).
1.1.2 Grey and White triangle patterns
1.1.2.1 Growth description
Grey triangles: Each diagram gains an additional row of triangles, where the added number
increases by 1 more than the previous increase.
White triangles: Begins adding from Diagram 3 onwards, with each subsequent diagram
adding one more triangle than the previous addition (similar growth to Grey but starting
later).
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 Analysis of Patterns
1.1.1.1 First differences (1)
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
Differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19)
Differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Disclaimer:
Grey trianglesprovided
The materials (0, 1, 3,are
6, 10, 15, 21,
intended for28, 36, 45) and informational purposes only. They should not be
educational
Differences:
submitted as 1, 2, 3, 4,
original 5, 6,
work or7, 8, 9in violation of any academic institution's policies. The buyer is solely
used
responsible for how the materials are used.
White triangles (0, 0, 1, 3, 6, 10, 15, 21, 28, 36)
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 Analysis of Patterns
1.1.1.1 First differences (1)
Small triangles (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
Differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles (1, 3, 5, 7, 9, 11, 13, 15, 17, 19)
Differences: 2, 2, 2, 2, 2, 2, 2, 2, 2
Grey triangles (0, 1, 3, 6, 10, 15, 21, 28, 36, 45)
Differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
White triangles (0, 0, 1, 3, 6, 10, 15, 21, 28, 36)
Differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
1.1.1.2 Classification
• Small triangles: Quadratic (second differences constant)
• Black triangles: Linear (first differences constant)
• Grey triangles: Quadratic (second differences constant)
• White triangles: Quadratic (second differences constant)
, 1.1.1.3 Justification
The Black triangles pattern has a constant first difference (2), indicating a linear sequence
where each term increases by the same amount. The Small triangles pattern has first
differences (3,5,7,9...) that themselves increase consistently, indicating a quadratic sequence
because the second difference is constant (always 2).
1.1.2 Grey and White triangle patterns
1.1.2.1 Growth description
Grey triangles: Each diagram gains an additional row of triangles, where the added number
increases by 1 more than the previous increase.
White triangles: Begins adding from Diagram 3 onwards, with each subsequent diagram
adding one more triangle than the previous addition (similar growth to Grey but starting
later).
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
