36 students are rehearsing for the National Day Parade. Their teacher wants to arrange them into equal rows for a formation. The arrangement must follow two rules: Each row must have MORE THAN 1 student. There must be MORE THAN 1 row. How many different arrangements are possible?
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Worked Solution
Step 1: Find ALL factors of 36 systematically.
36 / 1 = 36 — factor pair (1, 36)
36 / 2 = 18 — factor pair (2, 18)
36 / 3 = 12 — factor pair (3, 12)
36 / 4 = 9 — factor pair (4, 9)
36 / 5 = 7.2 — NOT a whole number, skip
36 / 6 = 6 — factor pair (6, 6)
All factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36}
Step 2: Apply the two rules.
Rule 1 — More than 1 student per row: remove 36 (that gives 1 student per row).
Rule 2 — More than 1 row: remove 1.
Remaining valid row counts: {2, 3, 4, 6, 9, 12, 18}
Step 3: Count.
7 arrangements.
Answer: 7 different arrangements are possible.
Correct answer: 7
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