Dimensions of a figure
I have a 112-dimensional figure. I select random 113 points on it. What is the avg.area of all good figures, good figures are figures that when I join them to form a 113-gon figure, the center of the figure lies inside the 113-gon shape?
In other words, find the avg. portion it covers the figure and thus it shows the same as the probability.
If the answer can be expressed as for integers and , with positive and as small as possible, submit your answer as .
This is a remake of one of the Putnam Integral Exam, this is the harder sum of the hardest sum from the Hardest exam in the world.Enjoy!
The answer is 56.
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1 solution
I can select 113 points but a point will be dependent on the rest 112 points.So, the formula will be (1/2)^112 and so 1/2 * 112 = 56 so the answer.Let's see who proves the formula.