### 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?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# 2011 Digits

##### Stage: 4 Short Challenge Level:

$20 \div 11 = 1\frac{9}{11} = 1.81818181...$. So the first 2011 digits are 1006 '1's and 1005 '8's. Therefore the required total is $1006\times1 + 1005\times8 = 1006 + 8040 = 9046$.

This problem is taken from the UKMT Mathematical Challenges.