### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

### Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

### Maximum Flow

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

##### Age 16 to 18 Challenge Level:

In this problem a circuit has been set up to mimic a simple adding machine but the logic gates have all been set to AND by mistake.

By clicking on the blue squares you can change the type of logic gates.

There are three switches which you can turn on or off. There are two bulbs: one on the right and one on the left.

Can you find the combination of gate types such that:

• no bulb is on if no switch is on,
• the left-hand bulb is on and the right-hand bulb is off when exactly one switch is on
• the right-hand bulb is on and the left-hand bulb is off when exactly two switches are on
• and both bulbs are on if all three switches are on.

What do you think that this circuit represents?

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You can read more about the mathematical aspects of logic and circuits in our article .