### Even Up

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

### Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

### Greetings

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How many such students are there?

# Mathland Election

##### Age 11 to 14 Challenge Level:

On Mathland TV a political commentator summed up an election result as follows.

A Labour majority of $1729$ last time has been turned into a Conservative majority of $1654$ in this election and the conservative candidate has obtained $38\%$ of the poll. Labour has taken second place. The Liberal Democrat has obtained only $14\%$ of the poll and has been beaten into fourth place by the SNP candidate who has $50$ more votes than the Liberal Democrat.

Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.
[This question comes from the book 'Mathematical Challenges' published in 1989 for the Scottish Mathematical Council by Blackie, ISBN 0216 92622X]