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Finding nth Fibonacci Number using Golden Ratio:



Following is another mathematically correct way to find the same.



nth Fibonacci Number Fn = fib1.


Here φ is golden ratio with value as fib2.



The above formula seems to be good for finding nth Fibonacci Number in O(Logn) time as integer power of a number can be calculated in O(Logn) time. But this solution doesn’t work practically because φ is stored as a floating point number and when we calculate powers of φ, important bits may be lost in the process and we may get incorrect answer.




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Measuring Time Logic Puzzle You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes.

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