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'Not Another NAND!' printed from http://nrich.maths.org/
A good way to start these problems is by experimenting with logic
Start by looking at ways to link up two NAND gates using either 1
or 2 input switches.
You will clearly need to understand how the target output gates
AND, OR, NOT etc. work before attempting this
The sort of thinking used in this
problem is typically formally found in Decision Mathematics
Modules, but can be attempted with only a simple knowledge of logic
gates and truth tables.