A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
Be patient this problem may be slow to load.
Primes and Six
Age 14 to 16 Short Challenge Level
Let $p$ and $q$ be prime numbers with $q=p+2$ and $p$ greater than $3$.
Prove that $pq+1$ is divisible by $36$.
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.