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#### find_the_fun

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- Feb 1, 2012

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A circuit has n switches, all initially off. In order to be able to flip the

I got \(\displaystyle f_n=f_{n-1}+2\) with initial condition \(\displaystyle f_1=1\) Is this right? This makes sense because to get the

*i*th switch, the (*i-1*)th switch must be on and all earlier switches off. The first switch can always be flipped. Find a recurrence relation for the total number of times the*n*switches must be flipped to get the*n*th switch on and all the others off.I got \(\displaystyle f_n=f_{n-1}+2\) with initial condition \(\displaystyle f_1=1\) Is this right? This makes sense because to get the

*n*th switch on, you need the (*n-1*)th switch on, and then you need to turn on the*n*th switch itself and turn off the (*n-*1)th switch. I have trouble explaining this using math though.
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