### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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?

### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

# Factorised Factorial

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

For a positive integer $n$, we define $n!$ to be the product of all the positive integers from $1$ to $n$; that is $n!=1\times 2\times 3\times\ldots\times n$.

If $n!=2^{15}\times 3^6\times 5^3\times 7^2\times 11\times 13$, what is the value of $n$?

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.