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With OR and AND for the switches:
when both switches are off both bulbs are off,
when either switch is on one bulb is on,
when both switches are on both bulbs are on.
With AND and AND for the switches:
when both switches are on both bulbs are on,
the rest of the time - both bulbs are off.
With NOR and NOR for the switches:
when both switches are off both bulbs are on,
the rest of the time - both bulbs are off.
With XOR and OR for the switches:
when both switches are off both bulbs are off,
when one switch is on both bulbs are on,
when both switches are on one bulb is on.
Simple Counting Machine
Age 11 to 16
Challenge Level 
Well done to Chris from CSN for a clear explanation on how to solve the first question, and well done to Jake from Crosscrake C.E. School, Louise from Melling St.Wilfreds School and Tristan from St James School for answering the first three questions correctly. Special congratulations go to Rachel from Tatham Fells School who managed to answer all questions correctly. Here are her solutions:
With OR and AND for the switches:
when both switches are off both bulbs are off,
when either switch is on one bulb is on,
when both switches are on both bulbs are on.
With AND and AND for the switches:
when both switches are on both bulbs are on,
the rest of the time - both bulbs are off.
With NOR and NOR for the switches:
when both switches are off both bulbs are on,
the rest of the time - both bulbs are off.
With XOR and OR for the switches:
when both switches are off both bulbs are off,
when one switch is on both bulbs are on,
when both switches are on one bulb is on.
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