You may also like

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 Short
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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Copyright © 1997 - 2023. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.