A Christmas tree is decorated with 36 lights, which are numbered 1 through 36. T

Question

A Christmas tree is decorated with 36 lights, which are numbered 1 through 36. Timers are set so that every 5 minutes a change occurs in the light patten. The sequence of changes reperats every 3 hours.
Switches are set so that:
At the end of the first time interval, every light is turned on.
At the end of the second time interval, every second switch is reversed.
At the end of the third time interval, every third switch is reversed.
Etc.

Question:
a) What is the state of the lights at the end of the first 3 hours (after the 36th time interval)?

b)If the tree had n lights, what is the state after n time intervals?

Explanation / Answer

a. every third swith is reversed b. every n/12 switch is reveresed

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