### Teddy Town

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

# Circuit Maker

##### Stage: 3, 4 and 5 Challenge Level:

A circuit is a set of switches, wires, bulbs and components called logic gates .

There are seven different types of logic gates, each with a technical-sounding name:
AND
OR
XOR (exclusively OR)
NAND (not AND)
NOR (not OR)
XNOR (not XOR)
NOT

One wire comes out of each logic gate and in the examples below this wire is always attached to a bulb. The bulb is on or off depending on the inputs from the switches and the type of logic gate.

Here is a circuit containing one of each type of gate wired up to a bulb.

By clicking the switches on or off (using the blue square in their top left hand corners), can you work out what each of the different logic gates does?

Full Screen Version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

Now that you are familiar with the properties of the gates you can experiment by building your own circuits with interesting properties using the interactivity below. Instructions are given at the bottom of the page. You can find some ideas and challenges in Simple Counting Machine

You can also read and learn more about logic circuits and gates and mathematical logic in the article Logic, Truth Tables and Switching Circuits .

Full Screen Version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

INSTRUCTIONS

To build a circuit follow these steps. You can delete mistakes by clicking on the cross which appears when you hover above the icon.

1. Left-click on the components to drag them on to the circuit board space.

2. FIRST click next to a red dot and drag to the right to create a wire; THEN you can stretch this wire to join with any other red dot in the circuit.

3. Click on the switches to turn them on or off. Wires 'fill' with current unless blocked by an un-triggered logic gate.

4. Click on the logic gates to change their type.

5. Left-click and drag to move the components around.

The key ideas are shown in this picture; by clicking on the triangle you can also watch a short video clip (1Mb) of the creation of the circuit.

If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.