Challenge Level

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?

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.