Indivisible
Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?
Age
14 to 16
Challenge level
Problem
Some students (fewer than $100$) are having trouble lining up for a school production.
When they line up in $3$s, two people are left over.
When they line up in $4$s, three people are left over.
When they line up in $5$s, four people are left over.
When they line up in $6$s, five people are left over.
How many students are there in the group?
Student Solutions
Answer: 59
Lining up in rows of 3:
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Lining up in rows of each number:
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What comes next in each pattern?
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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.