100 Examples of sentences containing the common noun "pigeonhole principle"

Definition

The "Pigeonhole Principle" is a fundamental concept in combinatorics that states if ( n ) items are put into ( m ) containers (or "pigeonholes") and if ( n > m ), then at least one container must contain more than one item. This principle is often used to demonstrate the inevitability of certain outcomes in various mathematical and logical contexts.

Synonyms

Dirichlet's box principle
Box principle
Counting principle

Antonyms

None (The Pigeonhole Principle is a unique concept with no direct antonyms)

Examples

The Pigeonhole Principle illustrates that if you have 10 pairs of socks and only 9 drawers, at least one drawer will contain more than one pair.
In a classroom, the Pigeonhole Principle suggests that if there are 30 students and only 29 chairs, at least one chair must be shared.
During the math competition, the Pigeonhole Principle was used to prove that at least two participants must have the same birthday.
The researchers relied on the Pigeonhole Principle to argue that among 13 people, at least two must have the same number of hairs on their heads.
By applying the Pigeonhole Principle, we can conclude that in a group of 1,000 people, at least two must live in the same city.
The Pigeonhole Principle can help in understanding why certain distributions are inevitable in large datasets.
When studying social networks, the Pigeonhole Principle helps to show that connections between individuals will often overlap.
The Pigeonhole Principle is frequently used in computer science to analyze data distribution.
In a simple experiment, the Pigeonhole Principle demonstrated that if 5 balls are placed in 4 boxes, at least one box must contain at least 2 balls.
The Pigeonhole Principle asserts that in any scenario where items are distributed among containers, overlaps are unavoidable under certain conditions.
A common application of the Pigeonhole Principle is in proving the existence of duplicate entries in a dataset.
The Pigeonhole Principle can be illustrated through everyday examples, making it accessible to students.
The mathematician explained how the Pigeonhole Principle applies to voting systems and election outcomes.
In a game of cards, the Pigeonhole Principle indicates that if there are more players than card types, some players will have the same type.
To make a point about resource allocation, the speaker referenced the Pigeonhole Principle.
The Pigeonhole Principle can be applied in cryptography to show that certain keys must repeat.
In the context of genetics, the Pigeonhole Principle helps explain why certain traits appear in populations.
The Pigeonhole Principle is a powerful tool for proving statements in number theory.
When discussing databases, the Pigeonhole Principle reveals the likelihood of data redundancy.
The Pigeonhole Principle often serves as a starting point for more complex mathematical proofs.
The teacher used the Pigeonhole Principle to explain why collaboration leads to overlapping ideas.
The Pigeonhole Principle is essential in probability theory for calculating outcomes.
The workshop on combinatorics included a section on the Pigeonhole Principle.
In a coding challenge, the Pigeonhole Principle was critical for optimizing storage solutions.
The Pigeonhole Principle can be visualized using simple diagrams to aid understanding.
The Pigeonhole Principle suggests that in any large enough group, similarities are bound to emerge.
Analyzing the survey results, the researchers applied the Pigeonhole Principle to interpret the data.
The Pigeonhole Principle can be evident in real-life scenarios, such as seating arrangements.
The author wrote about the Pigeonhole Principle in relation to statistical anomalies.
The Pigeonhole Principle provides a logical framework for understanding distribution patterns.
In software testing, the Pigeonhole Principle can explain why certain bugs recur.
The Pigeonhole Principle was used to demonstrate the limits of predictive modeling.
The principle has been a topic of discussion in many mathematics classrooms, showcasing the Pigeonhole Principle.
The Pigeonhole Principle is a fascinating concept that has applications beyond mathematics.
By employing the Pigeonhole Principle, we can simplify complex problems into manageable parts.
The Pigeonhole Principle was essential in determining the outcome of the logistics plan.
In a research paper, the author explored the implications of the Pigeonhole Principle on data analysis.
The Pigeonhole Principle is often a surprise to students learning about probability for the first time.
The workshop showcased the Pigeonhole Principle as a means to unlock creative solutions.
The Pigeonhole Principle can often lead to surprising conclusions in statistical studies.
The engineer applied the Pigeonhole Principle to enhance the efficiency of the system design.
During the conference, the Pigeonhole Principle was highlighted as a key concept in problem-solving.
The Pigeonhole Principle is foundational in understanding limitations in various fields.
By exploring the Pigeonhole Principle, students gain insight into logical reasoning.
The Pigeonhole Principle serves as a reminder that some overlaps are inevitable in life.
The team used the Pigeonhole Principle to justify their findings in the project report.
The concept of the Pigeonhole Principle often leads to deeper discussions about mathematics.
The Pigeonhole Principle can sometimes produce counterintuitive results.
In a game theory scenario, the Pigeonhole Principle helps analyze player strategies.
The mathematician shared examples of the Pigeonhole Principle in everyday life.
The Pigeonhole Principle provides a lens through which to view complex systems.
The study of the Pigeonhole Principle enhances critical thinking skills among students.
The Pigeonhole Principle was a key argument in the lawyer's case.
Using the Pigeonhole Principle, we can demonstrate the necessity of redundancy in systems.
The Pigeonhole Principle highlights the importance of resource management in economics.
The teacher challenged students to apply the Pigeonhole Principle in real-world scenarios.
The Pigeonhole Principle can help simplify complex mathematical proofs.
The Pigeonhole Principle was an integral part of the innovative solution proposed.
The presentation on the Pigeonhole Principle captivated the audience.
The Pigeonhole Principle is often overlooked but has significant implications.
By understanding the Pigeonhole Principle, one can better navigate competition.
The Pigeonhole Principle serves as a cautionary tale in resource allocation.
The researcher asserted that the Pigeonhole Principle would apply to their hypothesis.
The Pigeonhole Principle is a valuable concept for understanding social dynamics.
In the seminar, the Pigeonhole Principle was discussed in relation to decision-making.
The Pigeonhole Principle can provide clarity in seemingly chaotic systems.
The professor emphasized the Pigeonhole Principle during the lecture on combinatorics.
The Pigeonhole Principle can lead to breakthroughs in various scientific fields.
The application of the Pigeonhole Principle in artificial intelligence was intriguing.
The Pigeonhole Principle has become a staple in mathematics education.
The Pigeonhole Principle illustrates the importance of consideration in planning.
In analyzing customer data, the Pigeonhole Principle helped identify patterns.
The Pigeonhole Principle can challenge our assumptions in statistical modeling.
The concept of the Pigeonhole Principle encourages innovative thinking.
By utilizing the Pigeonhole Principle, we can forecast trends with greater accuracy.
The Pigeonhole Principle provides a framework for understanding population distributions.
The student successfully applied the Pigeonhole Principle in their research project.
The Pigeonhole Principle emphasizes the need for thorough analysis in data interpretation.
The Pigeonhole Principle was pivotal in the discussion on resource distribution.
By applying the Pigeonhole Principle, the team was able to streamline their workflow.
The Pigeonhole Principle has relevance not only in mathematics but also in social sciences.
The Pigeonhole Principle can explain why certain trends emerge in consumer behavior.
The research highlighted the Pigeonhole Principle as a critical component of their findings.
The Pigeonhole Principle helps clarify the relationship between variables in statistics.
The Pigeonhole Principle serves as a reminder of the interconnectedness of systems.
The workshop included interactive exercises based on the Pigeonhole Principle.
The Pigeonhole Principle was a key element in the proposal's success.
The Pigeonhole Principle can illustrate the challenges of managing limited resources.
The importance of the Pigeonhole Principle in algorithm design cannot be overstated.
The Pigeonhole Principle was referenced in discussions on fairness and equity.
The Pigeonhole Principle has practical applications in various industries.
The implications of the Pigeonhole Principle extend to scientific research methodologies.
The Pigeonhole Principle provides essential insights into the nature of randomness.
The Pigeonhole Principle can be a powerful tool for innovation in product design.
The Pigeonhole Principle is often a topic of debate among mathematicians.
The Pigeonhole Principle can be used to simplify complex algorithms.
The Pigeonhole Principle serves as an illustration of fundamental truths in mathematics.
The Pigeonhole Principle was crucial in developing the new strategy for the project.
The Pigeonhole Principle offers a unique perspective on competition and collaboration.
The Pigeonhole Principle is an essential topic in the study of mathematics and logic.