# Probability of No Encounter Between Crawling Ants on a Polyhedron

• young e.
In summary: We are discussing the probability that no two ants will encounter each other when they are moving along the edges of a polyhedron. This probability is 2/8, as the only two cases where no encounter occurs is when the ants all go either left or right. For other cases, an encounter occurs. The question is then asked for different polyhedra, what is the probability that no two ants will encounter each other when moving along the edges. The answer should be given in its lowest reduced form.
young e.
Suppose there are ants at each vertex of a triangle and they all simultaneously crawl along a side of the triangle to the next vertex. The probability that no two ants will encounter one another is 2/8, since the only two cases in which no encounter occurs is when all the ants go left, i.e., clockwise -- LLL -- or all go right, i.e., counterclockwise -- RRR. In the six other cases -- RRL, RLR, RLL, LLR, LRL, and LRR -- an encounter occurs. Now suppose that, analogously, there is an ant at each vertex of a polyhedron and that the ants all simultaneously move along one edge of the polyhedron to the next vertex, each ant choosing its path randomly. For each of the following polyhedra, what is the probability that no two ants will encounter one another, either en route or at the next vertex? Express your answer reduced to lowest common denominators, e.g., 2/8 must be reduced to 1/4.

"Express your answer reduced to lowest common denominators, e.g., 2/8 must be reduced to 1/4" sounds like homework...

Where are the polyhedra?

EnumaElish said:
"Express your answer reduced to lowest common denominators, e.g., 2/8 must be reduced to 1/4" sounds like homework...

taka ra man ka... ingna lang gud nga dili ka ka answer,, ayaw sige ug pataka ug storya...

## 1. What is the "Probability of No Encounter Between Crawling Ants on a Polyhedron"?

The "Probability of No Encounter Between Crawling Ants on a Polyhedron" refers to the likelihood of two ants crawling on a polyhedron not crossing paths or encountering each other.

## 2. How is the probability of no encounter between crawling ants on a polyhedron calculated?

The probability of no encounter between crawling ants on a polyhedron is calculated by taking the total number of possible paths the ants could take on the polyhedron and dividing it by the total number of ways the ants could encounter each other.

## 3. What factors influence the probability of no encounter between crawling ants on a polyhedron?

The factors that influence the probability of no encounter between crawling ants on a polyhedron include the number of ants, the shape and size of the polyhedron, and the initial starting positions of the ants.

## 4. Can the probability of no encounter between crawling ants on a polyhedron be determined for any polyhedron?

Yes, the probability of no encounter between crawling ants on a polyhedron can be determined for any polyhedron as long as the number of ants and their starting positions are known.

## 5. Why is the probability of no encounter between crawling ants on a polyhedron an important concept in mathematics?

The probability of no encounter between crawling ants on a polyhedron is an important concept in mathematics because it helps us understand the likelihood of two events occurring simultaneously. It also has practical applications in fields such as computer science, where it is used in algorithms for pathfinding and collision detection.

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