### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

### DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

### Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

# Indivisible

##### Age 14 to 16 ShortChallenge 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.