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Weekly Problem 25 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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?

 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas. 
 
 

This problem is taken from the UKMT Mathematical Challenges.

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