### Two Trees

Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?

### Equation Attack

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

### Root Hunter

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

# Farey Approximation

##### Stage: 5 Short Challenge Level:
The lemon squeezer icon here is to suggest that you need to 'squeeze' the range in which the irrational number lies making this interval smaller and smaller to get better and better rational approximations.

To decide which interval to choose you may need to know the decimal expansion of the irrational number you are approximating (as in the case of $\pi$). In the case of an irrational number which is a square root you can square the inequalities and you don't need to know the decimal expansion.