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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?

Four Go

Age 7 to 11
Challenge Level
This was a good solution that was sent in this time.

Abigail and Amber from Harrison Primary School wrote this very comprehensive reply;

We first started to think about what numbers could and couldn't be made with the digits and operations given. We took out all of the prime numbers (momentarily) as we know that they have no factors (2, 3, 5, 7, 11, 13, 17). However as some of those numbers could be made by multiplying two other numbers together we re-added some of them in (2, 3, 5,). Then we found 4 numbers in row that could be made and went for them for the highest chance of winning.

In our opinion we think it doesn't matter if you go first or second ( as they both have there advantages). We thought about it logically and found all easy possibilities of a sequence of 4 in a row. To do this we took out prime numbers that had no factors and couldn't be made by multiplying 2 numbers together then we looked at 4 numbers in a row that could be made.
Now we looked at would it matter if you went 1st or second? As we started to dig deeper we realize that they both had there pros and cons. When you went first you had the choice of picking what row you wanted to go for, however then the other person could see what angle you were going for and block you immediately. Then its was the same for going 2nd, you could
easily block your opponent yet they got the first chose of there 4 in the row sequence.

Here are some oter solutions to consider from when the game has been "live" before.

Arti wrote to us to say:

There are two things that are not defined which need a definition:
- If player A marked a number in the number line, can player B mark it later?
- If player A used two numbers from the square, can player B use one or both those numbers?

These are good questions, Arti.  What did you decide in the game/s you played?  Did that work well?  You could try out both versions and decide which works better.

Rowena from Christ Church Primary told us:

I played this game with my Mum and neither of us won. We played it again and my Mum let me win!
We decided to list all the possible whole number answers. They were 2, 3, 4, 5, 6, 8, 9, 10, 12, 15 and 20. Once we knew these, it was easy to choose numbers to block the opponent and not let them get four in a row.
You can only win if your opponent makes a mistake or lets you win!

Thank you, Rowena - that was a good idea to make a list of the whole number answers.

I wonder whether you could change the game to make it a better game?