Circular Circuitry

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.

Possible approach

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 inconsistencies.

Key questions

• 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 on?

Possible extension

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?

Possible support

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?