Exercise #8 Solution

Light Switch Problem




This week's exercise centres around a classic logic puzzle:




A lot of switches




I have a board of light switches, numbered 0,1,2,...,1023.




Each light switch can be either on or off. All switches are initially off.




Step 1:




I flip all of the switches starting at 0.




At this point, all of the light switches are on.




Step 2:




I flip every second switch, starting at 0.




At this point, lights 0,2,4,6,8,... are off.




Lights 1,3,5,7,9,... are still on.




Step 3:




I flip every third switch, starting at 0.




So I flip switches 0,3,6,9,12,...




that is, if a switch is on, I flip it to off.




If a switch is off, I flip it to on.




...




Step 1023:




I flip every 1023'rd switch, starting at 0.




So I flip 0 and 1023.




Question: At this point, which switches are on and which are off?




Solve the Problem




Your rst task is to try to solve the puzzle using nothing but your own brain (and possibly a pen & paper). Can you gure out the pattern? (there's a way of nding the answer without actually walking through 1023 steps).




No... really... Solve the Problem




I'm sure half of you just jumped straight over the previous section to get to the \real" exercise. But really, c'mon... give it a try.



Building a switch




In a le called ex8.py, build a class LightSwitch with the following properties:




When I create a switch, I should be able to set it's default state by inputting a string \on" or \o ". I should be able to use a switch's turn on method to turn it on.




turn off should work the same way, but in the opposite direction.




I should also be able to call a flip method to ip its state (if it's on, it turns o ; if it's o , it turns on).




If I print a switch, it should print either I am on or I am off (whichever is currently true).




If I try to perform an illegal operation on a switch (e.g., turn a switch on when it's already on), nothing should happen.







One other thing (hope you read the instructions before you started coding). The switch shouldn't hold its state in a string. There's a better data type that a switch can use to keep track of its state.




Building a switch board




In your ex8.py le, build a class SwitchBoard with the following properties:




When I create a switchboard, I should be able to set the number of switches it contains. All switches should start in the "off" position.




If I print a switchboard, it should print something along the lines of: "The following switches are on: 0 2 4 6 8".




The which switch method should return a list of integers representing the switches that are on, in order(e.g., [1,3,5,7,9]).




If I call flip(n) with n as an integer, it should ip the state of the n'th lightswitch.




If I call flip every(n) with n as an integer, it should ip the state of every n'th lightswitch, starting at 0. So flip every(2) would ip switches 0, 2, 4, 6, etc.




The method reset(), should turn all switches o .




If I ask the switchboard to ip a switch which doesn't exist, nothing should happen (it shouldn't crash). You can add any extra methods you need to make the code work as described above.







Now check your solution




Now, write a piece of global code that solves the problem as stated above. Your code should not run when the automarker imports your le. Did you get it right? Can you see the pattern now? Do you understand why this pattern exists?






























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