Wikipedia shows us we can construct a two location multiway switching system with two 3-way switches:
They also teach us how to perform three location multiway switching with two 3-way switches and one 4-way switch:
Is it possible to make a similar system (three locations, all able to switch the light in any situation) with only three 3-way switches?
What can be said in general about the switches needed to make an n-location multiway switching system?
Answer
What you call "three-way" switches I'd call "two-way" switches because they switch one of two ways - just a minor thing really. The middle switch in the 3-location scenario can be made from 2 x 2-way switches but they need to be "ganged" so they both operate together: -
To make n-location switching you repeat the middle dual-switch circuit from above - two wires in and two wires out. Repeat n times. It's an Exclusive or function.
4-location switch: -
Is it possible to just use 1 x SPDT switch per position - I think not but i'd like to see it disproven
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