### 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