### 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:

We have received correct solutions from Sarah Dunn, Ben Falconer, Fern Smith and Ian Downie, all from Madras College. Well done to you all.

They all used a similar argument:

Conservative $38\%$ $38\% - 1654$ votes $14\% + 50$ votes $14%$

$38\% + 38\% -1654 +14\% + 50 + 14\% = 100\%$

$104\% - 1604 = 100%$

therefore $4\% = 1604$ votes

$1\% = 401$ votes

and $100\% = 40100$ total votes.

Therefore

Conservative Labour $38\%$ of $40100 =$ $15238$ votes $15238 - 1654 =$ $13584$ votes $5614 + 50 =$ $5664$ votes $14% of 40100 =$ $5614$ votes $40100$ votes