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'Circular Circuitry' printed from http://nrich.maths.org/
Why do this problem?
This problem presents a fascinating logical exercise. Forcing
students to deal with logical inconsistency will give an excellent
mental workout. Decisions need to be made as to how to decide on
'consistent' configurations. This will challenge students'
perceptions: the very simple concept of a logic gate can quickly
lead to deep logical issues.
This problem might create interesting discussion as students
struggle with understanding the behaviour of the circuits. See how
the discussion evolves. Try to encourage precision in the
statements from the students as they grapple with the
- What do you see?
- What will happen when a switch is flicked?
- Some wires contain 'trapped' current. Are these circuits
consistent without this trapped current?
- If a switch is switched on and then off, does the circuit
return to its original state?
- Clearly we could make these circuits out of physical wires and
gates. What would happen in real life if they were switched
This problem introduced the concept of feedback. Students might
like to try to design their own feedback circuits. Can they create
feedback circuits which are definitely consistent? Definitely
inconsistent? Can they create feedback circuits which do not return
to their original state if a switch is flipped on and then
immediately back off?
Encourage students to follow the imaginary path of an electron
around the circuits. Can this electron get through each gate or
not? If the electron can get back to its starting point then the
circuit is consistent? If it cannot get through a gate is the gate
on or off?