A Problem of Knot

TL;DR

This paper corrects a previously published solution to a classical probability problem involving tying grass blades, using basic knot theory to provide an accurate answer without advanced mathematical knowledge.

Contribution

The authors provide the first correct solution to a historical problem from a 1954 USSR publication, clarifying the probability of forming a ring when tying grass blades.

Findings

Corrected probability calculation for the grass tying problem

Application of basic knot theory to a classical problem

Clarification of the original problem's solution

Abstract

In this article, the authors give the correct answer to the following problem, which is presented in the well-known problem book "CHALLENGING MATHEMATICAL PROBLEMS WITH ELEMENTARY SOLUTIONS"? by A. M. Yaglom and L. M. Yaglom. There are six long blades of grass with the ends protruding above and below, and you will tie together the six upper ends in pairs and then tie together the six lower ends in pairs. What is the probability that a ring will be formed when the blades of grass are tied at random in this fashion? The solution in the above book needs to be corrected, and we will present a correct answer in this article. Therefore, we are the first persons to present a correct?answer to a problem in a book published in the USSR? in 1954. By following the original idea of this problem book, we present the correct answer without using knowledge of higher knowledge, although we used a very basic knowledge of the Knot theory.