### Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

# First Connect Three

##### Age 7 to 14 Challenge Level:
We had a number of really thorough solutions sent in, here is a selction.
Firstly from Class 6 from St Helen's C of E Primary School:

1. Add or subtract numbers according to what numbers are left on the grid;
2.Try to put counters on numbers which are close to each other on the grid;
3. If going first, try and get a number close to the middle of the grid;
4. Sometimes take risks as it is all about luck;
5. Don't just go across, go diagonally as well;
6. Try to block your opponent's counters;
7. Keep silent - don't tell your opponent what you are going to do;
8. Try to work out your opponent's strategy as well.

We all enjoyed the game!

Next, Danish from Ryerson School in Canada sent his thoughts:

My solution was to cover four positive integers in a "U" shape near the top row. Then I would start covering the most negative integers I could before the computer could because it usually tries to cover the same +/- integers in the same row/column that you have done before. That is how I won the game against the computer.

Pupils from Aldermaston School, namely Mary, Amelie, Hannah, Thomas and Sophie, wrote interesting things they had noticed/found out:

I found 12 hard to get because I didn't get many high numbers. I found 5 easy to get because there are lots of easy solutions to get 5.

The inside numbers are easiest to get because you can get three numbers in a row all around. The hardest numbers are on the outside because you can't get three in a row all the way round.

I find the inside numbers the easiest because you can get 3 in a row all around but the outside numbers are the hardest because you can not get 3 in a row all around.

The easiest number is 5 beacuse you have lots of different sums you can do to get to 5.

12 and -5 are the hardest numbers beacuse you can only do them once. 7 is the best number to aim for beacuse you can get to 7 in lots of ways.

12 is one of the hardest numbers when rolling a 1-6 dice, you should increase the height of a number on the chart and how many faces on the
dice.

Lastly Ollie from S.U.N School wrote:

The hardest numbers to get are -5 and 12. -5 is hard because you can only get it by using 1-6 and 12 is hard because you can only get it with 6+6.

The easiest numbers to get are 0 and 7. 0 is easy because you can make it six ways: 6-6, 5-5, 4-4, 3-3, 2-2, 1-1. And 7 is easy because you can make it six ways as well: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.