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A red sphere in the middle of many green spheres on a textured background.

A red sphere in the middle of many green spheres on a textured background.
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Let N be a positive multiple of 5. One red ball and N green balls are arranged in a line in random order. Let P(N) be the probability that at least 35 of the green balls are on the same side of the red ball. Observe that P(5)=1 and that P(N) approaches 45 as N grows large. What is the sum of the digits of the least value of N such that P(N)<321400? (AMC 12/AHSME 2016) See more

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