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Parity Lights

Published online by Cambridge University Press:  01 August 2016

Dennis Epple  and
Martin Kutz
Dennis Epple
Affiliation:
Freie Universität Berlin, Institut für Mathematik II, Arnimallee 3, D-14095 Berlin, Germany emails: epple@math.fu-berlin.de / kutz@math.fu-berlin.de
Martin Kutz
Affiliation:
Freie Universität Berlin, Institut für Mathematik II, Arnimallee 3, D-14095 Berlin, Germany emails: epple@math.fu-berlin.de / kutz@math.fu-berlin.de
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Extract

Almost everybody has a light in their house that can be switched on and off from two or more different places. If your electrician set up the wiring properly, you are able to toggle the light with every single switch, independent of the others' current configuration.

We may think of the switches as implementing a parity function. If we label the two positions of a switch by 0 and 1, the light is on if the sum of switch positions is even and off if this sum is odd (or vice versa). So in the common case of only two switches, ‘light on’ is just the binary relation xor. (Not all real-life installations are of this kind. We also find the binary and implemented in a few houses—which can be very annoying, and even dangerous, at nights.)

Type
Articles
Information
The Mathematical Gazette , Volume 88 , Issue 511 , March 2004 , pp. 46 - 56
Copyright
Copyright © The Mathematical Association 2004

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References

1. Bollobàs, Bèla Graph theory, Springer (1979).CrossRefGoogle Scholar
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3. Wilson, Robin J. Introduction to graph theory, Academic Press (1972).Google Scholar