3-input XOR gate use only NOR gate

Question

What's the minimum number of NOR gate needed to build a 3-input XOR gate using only NOR gate?

Information I know:

https://en.wikipedia.org/wiki/NOR_logic

A XOR B = [ ( A NOR A ) NOR ( B NOR B ) ] NOR ( A NOR B )

A XOR B XOR C = ( A XOR B ) XOR C

Using the above formulas, I can implement 3-input XOR with 20 NOR gates.

What I don't know:

What's the minimum number of NOR gate? Is there a simpler way to implement 3-input XOR gate?

• jsotola: what is A NOR A?
• Justme: How have you tried to solve this and where are you stuck? This is not a free homework solving service.
• the busybee: @jsotola This is an inverter.
• the busybee: Did you cite the wikipedia correctly?

Answer 1

A 3 bit XOR gate can be made using 10 NOR gates . enter image description here

• Elliot Alderson: Please don't hand out solutions to homework questions. Also, you need to provide a link or citation for the graphics you copied into your answer.