Question 5

We find a common property of numbers in yellow boxes.

Step 1 — Check the puzzle numbers

Look at the numbers in the left figure. Let us find the prime factors for each number. Let us count each number's prime factors. We count them even if they are the same.

For the number 105: $105 = 3 \times 5 \times 7$ This number has 3 prime factors.

For the number 20: $20 = 2 \times 2 \times 5$ This number has 3 prime factors.

For the number 30: $30 = 2 \times 3 \times 5$ This number has 3 prime factors.

For the number 28: $28 = 2 \times 2 \times 7$ This number has 3 prime factors.

For the number 125: $125 = 5 \times 5 \times 5$ This number has 3 prime factors.

For the number 18: $18 = 2 \times 3 \times 3$ This number has 3 prime factors.

Step 2 — Check the solution numbers

Look at the numbers in the right figure. Let us find the prime factors for each number. Let us count each number's prime factors. We count them even if they are the same.

For the number 8: $8 = 2 \times 2 \times 2$ This number has 3 prime factors.

For the number 105: $105 = 3 \times 5 \times 7$ This number has 3 prime factors.

For the number 70: $70 = 2 \times 5 \times 7$ This number has 3 prime factors.

For the number 30: $30 = 2 \times 3 \times 5$ This number has 3 prime factors.

For the number 70: $70 = 2 \times 5 \times 7$ This number has 3 prime factors.

For the number 28: $28 = 2 \times 2 \times 7$ This number has 3 prime factors.

Step 3 — Find the rule

We saw that all numbers in both figures have 3 prime factors. This is true for every yellow box. So, this is the rule for the puzzle.

Answer

(i) The rule is that each number in a yellow box has exactly 3 prime factors. (ii) We count these prime factors even if they are the same. (iii) For example, $8 = 2 \times 2 \times 2$, which has 3 prime factors.