### 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?

# Consecutive Seven

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

Start with the numbers from $0$ - $20$:

Can you arrange these numbers into seven sets of three numbers, so that the totals of the sets are consecutive?

For example, one set might be $\{2, 7, 16\}$

$2 + 7 + 16 = 25$

another might be $\{4, 5, 17\}$

$4 + 5 + 17 = 26$

As $25$ and $26$ are consecutive numbers these sets might be part of your solution.

Once you've found a solution, here are some questions you might like to consider:

• Is there more than one possible set of seven consecutive totals? How do you know?
• Is there more than one way to make the seven totals?
• Could you make seven sets that all had the same total?
• Could you make seven sets whose totals went up in twos? Or threes? Or...