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Step 3: Multiply the numbers by the number of times they appear
125 × 12 = 1500
250 × 9 = 2250
500 × 6 = 3000
1000 × 1 = 1000
Step 4: Add the results
1500 + 2250 + 3000 + 1000 = 7750
Final Answer: The total sum for Pattern f is 7750

Question: Which of the following patterns involves squares with dots that have different
colours representing different groups?
A. Pattern a
B. Pattern c
C. Pattern d
D. Pattern e
Explanation
C. Pattern d
- Identify the squares with different coloured dots.
- Count the number of squares for each colour.
- Multiply the number of squares by the number of dots in each square.
- Add the results to find the total number of dots in the pattern.

An Unsolved Mystery - the Collatz Conjecture
The Collatz Conjecture is an intriguing mathematical sequence that remains unsolved. Here's
how the sequences work:
Sequences Examples:
 Sequence a: 12, 6, 3, 10, 5, 16, 8, 4, 2, 1
 Sequence b: 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
 Sequence c: 21, 64, 32, 16, 8, 4, 2, 1
 Sequence d: 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
Rule Applied:
 Even Number: Divide by 2.
 Odd Number: Multiply by 3 and add 1.
 Repeat: Continue applying the rule to the result.
Each sequence, no matter what number you start with, eventually reaches 1. This observation
is central to the Collatz Conjecture.