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A classic logic puzzle presents a scenario where you must identify which of three switches controls three separate light bulbs in the attic, with only one trip allowed upstairs. In addition, a mathematical challenge requires you to fill in numbers within the constraints of a circle puzzle where each number from 1 to 9 can only be used once. Use deductive reasoning and mathematical skills to solve both challenges efficiently.
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Puzzle A Puzzle B
There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?
The number within the 4 sectors of the outer circle is equal to the sum of the three numbers in its sector. The numbers in the individual circles can only be 1 to 9 and each number can be used only once. One number has been provided to get you started. Find the remaining 4 numbers.