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Broad Topics > Calculations and Numerical Methods > Approximate solution by numerical methods.

### Root Hunter

##### Stage: 5 Challenge Level:

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

### Equation Attack

##### Stage: 5 Challenge Level:

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.

##### Stage: 4 Challenge Level:

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?

### The Fastest Cyclist

##### Stage: 4 Challenge Level:

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

### Weekly Challenge 16: Archimedes Numerical Roots

##### Stage: 5 Challenge Level:

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

### Farey Approximation

##### Stage: 5 Short Challenge Level:

Use Farey sequences to obtain rational approximations to irrational numbers.