### BT.. Eat Your Heart Out

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

### Approximations, Euclid's Algorithm & Continued Fractions

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

### Euclid's Algorithm II

We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.

# Euclid's Algorithm and Musical Intervals

##### Stage: 5 Challenge Level:

See the problem Tuning and Ratio in which you have to find a decimal approximation for this ratio using logarithms. Here you must find an approximation in the form of a ratio of two integers without using logarithms.

You could use the same method as given for finding rational approximations to $\pi$ in the article Approximations, Euclid's Algorithm and Continued Fractions.