e-hm-selo - Sets and Logic MHF3202 4628 Home-E Prof. JLF...

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Sets and Logic MHF3202 4628 Home-E Prof. JLF King Friday, 18Apr2008 Essay question: Carefully Type a triple–spaced, grammatical, essay solving the problem. I suggest L A T E X but it is not required. This final-project is due by 2PM, Friday, 25Apr2008 , slid completely under my office door, LIT402. E1: Rabbits and Lights : Stretching off to your right are lights L 1 ,L 2 ,L 3 ,... . Each light has a button; if you press&release it, the light illuminates; push again, it is extinguished. Press again, it lights up. Off to your left are a queue of rabbits; so we have ...R 3 R 2 R 1 L 1 L 2 L 3 L 4 ,... All the lights are initially off. Then rabbit R 1 jumps on lights ( well –on the buttons, actually ) L 1 ,L 2 ,L 3 ,... , turning them all on. Now R 2 jumps on every 2 nd -light; L 2 ,L 4 ,L 6 ,... . At this point, the odds are illuminated and the evens are dark. Now, rabbit R 3 jumps on every 3 rd -light; L 3 ,L 6 ,L 9 ,... . Etc. . In general, R n jumps on lights L n ,L 2 n ,L 3 n ,L 4 n ,... . a
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