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Coconut Problem

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An island is inhabited by five men and a pet monkey. One afternoon the men gathered a large pile of coconuts which they proposed to divide equally among themselves the next morning. During the night one of the men awoke and decided to help himself to his share of the nuts. In dividing them into five equal parts he found that there was one coconut left over. This one he gave to the monkey. He then hid his one fifth share leaving the rest in a single pile. Later during the night another man awoke with the same idea in mind. He went to the pile, divided it into five equal parts, and found that there was one coconut left over which he gave to the monkey. He then hid his collection and leaving the rest in a single pile. During the same night each of the other three men arose, one at a time, and in ignorance of what had happened previously, went to the pile and followed the same procedure. Each time one coconut was left over. The next morning all five men went to the diminished pile and divided it into five equal parts, finding that one nut remained. What is the least number of coconuts the original pile could have contained?

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Solution Summary

A problem is solved using series.

Solution provided by:
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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