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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.

Why do this problem?

This problem is a complex exercise in logical manipulation. It will demand clear thinking on the part of the students.

Possible approach

Some time will need to be spent in understanding the description of the problem; students will need to be familiar with the logic gates and their meanings.

Students might have difficulty understanding the conditional statements 'If .... Then ....'

They should be encouraged to break down the statement into small parts and interpret the language very precisely.

Key questions

The key to this problem is clear, systematic logical thinking and breaking down the problem into manageable chunks
• What are the key features of the problem? What are we to change? What is fixed?
• What are the possible 'gates'?
• How many 'degrees of freedom' are there? How many constraints need to be met?
• In what way does this represent an 'adding machine'?

Possible extension

• Try the follow up question Circular Circuitry.
• Investigate other possible bulb outputs. Can the gates be chosen such that the bulbs are always on? always off?
• [hard] By linking together a sequence of these circuits, can students devise a way in which the total on 7 bulbs could be added up?

Possible support

For a simpler related problem, first try Simple Counting Machine