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Answer: 59
Lining up in rows of 3:
Lining up in rows of each number:
What comes next in each pattern?
Next number is a multiple of 3, 4, 5, 6
Lowest common multiples of 3, 4, 5, 6: 60, 120, 180, etc.
Fewer than 100 students $\therefore$ there are 59 students.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.