A 10,958 Solution - Numberphile

18 Apr 201706:46

TLDRIn this Numberphile video, the presenter explores the challenge of getting as close as possible to the number 10,958 using basic arithmetic operations and concatenation. Initially avoiding the use of powers to prevent computational issues, the presenter demonstrates various attempts to reach the target number. Through a process of trial and error, they eventually find a solution that involves concatenating numbers and performing arithmetic operations, successfully getting very close to the desired number. The video highlights the importance of embracing failure and trying unconventional methods, as they lead to the discovery of a creative solution that fills a previously unattainable gap.


  • 🔢 The challenge is to get as close as possible to the number 10,958 using basic arithmetic operations and concatenation.
  • ✅ Allowed operations include addition, subtraction, multiplication, and division, with the option to use brackets to dictate order.
  • 🚫 The use of powers is allowed but not utilized in this instance due to the complexity it adds to programming solutions.
  • 🔣 Concatenation is a valid operation in this challenge, despite not being explicitly stated, and is represented by two lines.
  • 🤔 The script discusses the arbitrary nature of including concatenation as a step in calculations, as it's more often used in setup.
  • 📈 An initial attempt at the challenge uses concatenation and arithmetic operations to get close to the target number but falls short at 10,958.4.
  • 💡 The presenter suggests that taking concatenation seriously can bridge the gap and achieve the exact target number.
  • 🎯 A revised approach using concatenation and arithmetic operations successfully reaches the number 10,958.
  • 👕 There's a humorous mention of Parker Square t-shirts being worn by viewers, indicating a community around the concept.
  • 🛍 The presenter playfully suggests selling t-shirts but acknowledges it might not be necessary.
  • 📚 The importance of trying and embracing failure in the pursuit of a solution is highlighted as a key takeaway from the Parker Square concept.

Q & A

  • What mathematical operations are allowed in the challenge described in the video?

    -The mathematical operations allowed in the challenge include addition, subtraction, multiplication, division, and the use of brackets to dictate order of operations. Concatenation is also allowed, which is the joining of numbers without mathematical operations.

  • Why is the concept of concatenation considered strange in the context of the video?

    -Concatenation is considered strange because there is no universally agreed-upon symbol for it, and it is not typically used as a step during calculations but rather in setting up the numbers for other operations.

  • What does the speaker mean by 'Parker Square'?

    -The term 'Parker Square' seems to be a colloquial or humorous reference to a square or a solution that is close to the target but not quite perfect, as indicated by the speaker's attempt to get as close as possible to the number 10,958.

  • What is the significance of the number 10,958 in the video?

    -The number 10,958 appears to be the target number that the speaker is trying to reach using the allowed mathematical operations and concatenation.

  • What is the speaker's initial attempt to reach the number 10,958?

    -The speaker's initial attempt involves concatenating 12, then multiplying by 3, 4, dividing by 5, multiplying by 6, 7, adding 8, and finally multiplying by 9. The result is close but not exactly 10,958.

  • Why does the speaker decide not to use powers in the challenge?

    -The speaker decides not to use powers because when writing a program to perform the calculations, they can lead to extremely large values that make the process more complicated and less manageable.

  • What is the final solution the speaker proposes to reach the number 10,958?

    -The final solution involves concatenating 1 with 2, then adding 3, and using brackets to multiply 4 by 5, then by 6, and concatenating with 7, adding 8, and multiplying by 9 to reach the number 10,958.

  • What does the speaker suggest about the importance of trying even when the odds of success are low?

    -The speaker suggests that it's important to give things a try even if there's a high chance of failure, as sometimes it does work out, and it's a learning experience regardless.

  • What is the speaker's view on the use of concatenation in mathematical challenges?

    -The speaker believes that concatenation should be a fully-fledged function in mathematical challenges and should be taken seriously, as it can fill gaps in reaching a target number.

  • How does the speaker feel about people wearing Parker Square t-shirts to his shows?

    -The speaker feels honored that people wear Parker Square t-shirts to his shows, indicating that it's a significant and positive recognition from his audience.



🔢 Mathematical Operations and Concatenation

The speaker discusses the rules of a mathematical challenge where basic operations like addition, subtraction, multiplication, and division are allowed, along with the use of brackets to dictate order. However, powers are not used due to the complexity they introduce in programming. The concept of concatenation is explored, which is allowed but not explicitly stated in the rules. The speaker uses concatenation creatively to construct numbers and then applies mathematical operations to them. An example calculation is given where numbers are concatenated and then multiplied by nine, resulting in a close approximation to a target number, 10,958.


🎯 Embracing Concatenation for Mathematical Problem Solving

In this paragraph, the speaker delves deeper into the use of concatenation in solving the mathematical challenge. They point out that concatenation is often overlooked but can be a powerful tool when used correctly. The speaker provides a step-by-step breakdown of a calculation that involves concatenating numbers before performing multiplication and addition, which leads to the same target number, 10,958. The speaker emphasizes the importance of trying unconventional methods and embracing the possibility of failure as part of the learning process. They conclude by suggesting that the length of the number could be determined using logarithms, hinting at a mathematical approach to quantify the complexity of the problem.




Concatenation refers to the act of linking or joining two or more things together, in this context, it refers to combining numbers to form a larger number without any mathematical operation in between. In the video, the concept of concatenation is crucial as it allows for the creation of numbers like '12345' from the individual digits '1', '2', '3', '4', and '5'. This is a key part of the puzzle in achieving the number 10,958 with the given operations.


In the context of this video, operations refer to the basic mathematical functions that can be performed on numbers, which include addition, subtraction, multiplication, and division. These operations are the building blocks for constructing the desired number through a sequence of calculations, as demonstrated by the various steps taken to approximate 10,958.


Brackets in mathematics are used to group expressions together, ensuring that the operations within the brackets are performed before moving on to other calculations outside of them. In the video, the use of brackets is essential for determining the correct order of operations to achieve the desired numerical outcome.


Powers, or exponentiation, is the operation of multiplying a number by itself a certain number of times. Although the video mentions that powers are allowed in the mathematical puzzle, the speaker chooses not to use them to avoid overly complex calculations. Powers are a way to significantly increase a number's value in a calculation.

💡Parker Square

Parker Square is a term used in the video to refer to the mathematical puzzle being solved. It is a play on words, combining the name 'Parker' with the concept of a 'square', which could be a reference to squaring numbers or a square root, both of which are mathematical operations. The term is used to add a personal touch to the problem-solving narrative.


The rules in this video are the constraints and permissions that guide the mathematical operations one can perform to reach the target number. They include the use of basic arithmetic operations, concatenation, and the use of brackets to dictate the order of operations. The rules are fundamental to the structure of the puzzle and the strategies used to solve it.


In the context of the video, 'explode' is a colloquial term used to describe the situation where a mathematical operation, particularly involving powers, results in an extremely large number that becomes difficult to handle or compute. The speaker mentions avoiding powers to prevent such an 'explosion' of values.



Approximation in mathematics is the process of finding a number that is close to the actual number being sought but not exact. In the video, the goal is to approximate the number 10,958 using the allowed operations and concatenation. The process involves a series of calculations that aim to get as close as possible to the target number.


A logarithm is the inverse operation to exponentiation, expressing the power to which a number (the base) must be raised to produce another number. In the video, the speaker mentions the use of a logarithm as a method to determine the length or size of a number in a calculation, which can be useful in solving complex mathematical problems.


Morale in the video is discussed in the context of problem-solving attitude. It refers to the motivation and encouragement one gives oneself to attempt a difficult task, even when the chances of failure are high. The speaker uses the term to emphasize the importance of perseverance and a positive approach to challenges.


The mention of a T-shirt in the video serves as a light-hearted aside, indicating the popularity and community engagement of the show. It shows that viewers are not just watching but also actively participating by wearing merchandise related to the show, which is a sign of support and shared interest in the content.


The challenge is to get as close to 10,958 using basic arithmetic operations and concatenation.

Concatenation is allowed but not explicitly stated in the rules.

Powers are allowed but not used to avoid large values in programming.

The use of brackets to determine the order of operations is highlighted.

A creative approach to concatenating numbers is demonstrated with 3, 4, 5, 6.

The presenter's initial attempt at the solution is described.

The process involves concatenation, multiplication, division, and addition.

The result of the initial attempt is 10,958.4, which is close but not exact.

The presenter discusses the importance of trying even if failure is likely.

A new approach is introduced with a different sequence of operations.

The presenter simplifies the calculation step by step.

The final result using the new approach is exactly 10,958.

The presenter emphasizes the significance of taking concatenation seriously in the solution.

The gap in the previous solution is filled by embracing concatenation.

The presenter shares the moral of the Parker square: to give it a go even when it might not work.

The presenter plans to submit the new solution, believing it to be correct.