A 10,958 Solution - Numberphile

In this Numberphile video, the host explores the challenge of getting as close as possible to the number 10,958 using basic arithmetic operations and concatenation. Initially, the host attempts a calculation that falls short but then refines the approach by incorporating concatenation more effectively. The video highlights the importance of not being afraid to try unconventional methods, even if they might fail, as they can sometimes lead to a successful solution. The final calculation cleverly uses concatenation and arithmetic to achieve the target number, demonstrating the power of creative problem-solving.

Takeaways

• 🔢 The challenge is to get as close as possible to the number 10,958 using basic arithmetic operations: addition, subtraction, multiplication, and division.
• 🚫 The use of powers is allowed but not utilized in this instance due to the complexity it adds to programming solutions.
• 🔄 Brackets are used to denote the order of operations, emphasizing the importance of sequence in calculations.
• 📝 Concatenation, or the joining of numbers to form a larger number, is a key part of the puzzle and is allowed in the rules.
• 🤔 The script discusses the ambiguity around the use of concatenation in mathematical operations, as it's not explicitly stated but implied through examples.
• 📈 The presenter attempts a solution using concatenation and basic arithmetic, resulting in a close approximation of the target number.
• 📉 The initial attempt falls short, yielding 10,958.4 instead of the exact number, highlighting the precision required in such problems.
• 💡 The presenter emphasizes the importance of trying different approaches, even if they seem unlikely to succeed, as part of the problem-solving process.
• 🎯 The final solution provided uses concatenation strategically along with arithmetic operations to achieve the exact number 10,958.
• 🤓 The script concludes with a moral lesson about embracing failure and trying multiple approaches in problem-solving, as success can come unexpectedly.
• 📚 The discussion also touches on the use of logarithms in determining the length or scale of numbers in mathematical problems.

Q & A

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

The mathematical operations allowed in the challenge are addition, subtraction, multiplication, division, and the use of brackets to determine the order of operations. However, powers are mentioned but not used in the script due to the complexity they add to programming.

What is concatenation in the context of the video?

In the context of the video, concatenation refers to the process of joining two numbers together to form a new number, such as combining '3' and '4' to make '34'. It is a method used in the challenge to create numbers from individual digits.

Why does the script mention that concatenation is a bit arbitrary and should be a fully-fledged function?

The script mentions that concatenation is a bit arbitrary because it is never explicitly stated as an allowed operation in the challenge's rules. It is used in the setup of numbers but not as a step during the calculation, which the speaker finds inconsistent and suggests it should be included as a formal operation.

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

The number 10,958 is the target number that the video's presenter is trying to reach using the allowed mathematical operations and concatenation. The presenter is attempting to get as close as possible to this number within the given rules.

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

The presenter's initial attempt involves a series of operations starting with the number 12, followed by concatenation with 2, multiplication by 3 and 4, division by 5, multiplication by 6 and 7, addition of 8, and finally multiplication by 9. The result is close to 10,958 but not exact.

What is the final solution presented in the video to reach the number 10,958?

The final solution involves concatenating 1 with 2, adding 3, and then performing operations in brackets: multiplying 4 by 5, multiplying by 6, concatenating with 7, adding 8, and multiplying by 9. This results in the exact number 10,958.

Why does the presenter mention that trying something where the odds of failure are high can be a good idea?

The presenter suggests that attempting something with high odds of failure can be beneficial because it encourages creativity and thinking outside the box. Sometimes, despite the odds, it can lead to a successful outcome, which is the case with the final solution presented.

What is the moral lesson that the presenter draws from the Parker Square challenge?

The moral lesson is to give it a go even when it seems like it might not work. Embrace the possibility of failure and learn from it, because occasionally, it can lead to success.

What does the presenter mean by 'Parker Square' in the context of the video?

In the context of the video, 'Parker Square' seems to be a reference to a challenge or a concept related to the mathematical operations and concatenation discussed. It might be a term used by the presenter to describe the process of trying to reach a specific numerical goal through creative mathematical means.

How does the presenter address the issue of not spelling out 'concatenation' in the challenge?

The presenter points out that while concatenation is not explicitly mentioned in the challenge's rules, it is used in the setup of numbers. The presenter suggests that if concatenation is included, it should be clearly stated and used as a step during calculations, not just in setup.

Outlines

00:00

🔢 Mathematical Operations and Concatenation

The speaker discusses the rules of a mathematical challenge where basic arithmetic operations (addition, subtraction, multiplication, and division) are allowed, along with the use of brackets to dictate order. Powers are permitted but not utilized due to the complexity they introduce in programming, leading to large values. The concept of concatenation is highlighted, where numbers are placed together without an agreed-upon symbol, and the speaker opts to use double lines to represent it. An example calculation is given, starting with the number 12, followed by a series of operations including concatenation, resulting in a close approximation to a 'Parker Square' number, which is a number that remains the same when its digits are rearranged.

05:01

🔍 Exploring Concatenation in Mathematical Expressions

This paragraph delves deeper into the use of concatenation within the mathematical challenge. The speaker notes that while concatenation is not explicitly forbidden, it is also not used as a step in calculations but rather in setting up numbers for other operations. The speaker then attempts to fill a perceived 'gap' in the challenge by taking concatenation seriously, providing an example where numbers are concatenated and then subjected to arithmetic operations. The process involves multiplying and adding numbers, followed by concatenation with additional digits, and concludes with a multiplication step. The result is a number that aligns with the 'Parker Square' concept, emphasizing the importance of embracing challenges and the potential for success even when failure seems likely.

Keywords

Concatenation

Concatenation refers to the operation of linking two sequences of characters or numbers together. In the context of the video, it is used to combine numbers in a way that they form a larger number without altering their order. For example, the script mentions '1 concatenate 2' to form the number 12. This concept is crucial for the video's theme, as it explores creative mathematical operations to achieve a specific numerical result.

Arithmetic Operations

Arithmetic operations encompass the basic mathematical functions of addition, subtraction, multiplication, and division. The video discusses these operations as part of the rules that can be applied to numbers to achieve a desired outcome. For instance, the script describes a process where numbers are multiplied and divided to get closer to the target number 10,958.

Brackets

Brackets in mathematics are used to group terms and dictate the order of operations. In the video, they symbolize the priority in which arithmetic operations should be performed. The script mentions using brackets to alter the sequence of operations, which is essential for reaching the numerical goal.

Powers

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, the script indicates that they are not used due to the complexity they add when programming. Powers are a fundamental concept in mathematics and could have been part of the solution if not for the decision to simplify the process.

Parker Square

Parker Square is a term used in the video, possibly referring to the presenter or a concept related to the mathematical puzzle. The script mentions 'classic Parker Square' and 'Parker Square t-shirts,' indicating it might be a recurring theme or a personal brand associated with the presenter. It adds a personal touch to the video's narrative.

Rules

The term 'rules' in the video refers to the constraints and permissions for the mathematical operations that can be performed. The script outlines that adding, subtracting, multiplying, dividing, and using brackets are allowed, while powers are not used. These rules set the framework within which the mathematical challenge is solved.

Exploding Values

In the context of the video, 'exploding values' likely refers to the phenomenon where numbers become excessively large, making calculations difficult or impractical. The script mentions avoiding powers to prevent such occurrences, which is a practical consideration in both programming and mathematical problem-solving.

T-shirt

A T-shirt in the video is mentioned as a merchandise item, suggesting that viewers might wear them to shows or as a sign of support. The script humorously discusses the idea of selling T-shirts, adding a light-hearted element to the video and engaging with the audience.

Moral

The moral of the story, as mentioned in the video, is the lesson or principle that can be taken away from the narrative. In this case, it is about embracing the challenge and giving it a go, even when the odds of success are low. The script uses the Parker Square puzzle as an example to illustrate this moral.

Logarithm

A logarithm is the inverse operation to exponentiation, used to determine the power to which a number must be raised to produce a given value. The script briefly mentions using a logarithm to calculate the length or base of a number, which is a mathematical tool relevant to the theme of the video.

Highlights

A mathematical challenge is presented to get as close as possible to 10,958 using basic arithmetic operations and concatenation.

Powers are allowed but not used due to the complexity they add to programming solutions.

Concatenation is a key part of the puzzle, despite not having a universally agreed-upon symbol.

The presenter's initial attempt at solving the puzzle involves a complex sequence of operations.

The result of the initial attempt is 10,958.4, which is very close to the target number.

The presenter discusses the importance of not being afraid to try methods that might fail.

A new approach is introduced, emphasizing the use of concatenation in the calculation.

The presenter simplifies the calculation by first performing arithmetic operations and then concatenating.

The final calculation is shown step by step, leading to the exact number 10,958.

The presenter emphasizes the gap in the puzzle was filled by taking concatenation seriously.

The moral of the Parker Square is highlighted: to try even if failure is likely, as success can be rewarding.

The presenter shares the method of finding the solution by embracing the possibility of failure.

The video concludes with the presenter's success in achieving the exact number 10,958.

The importance of including concatenation as a fully-fledged function in mathematical operations is discussed.

The presenter reflects on the arbitrary nature of including concatenation in the puzzle's rules.

The video ends with the presenter's enthusiasm for having successfully filled the gap in the puzzle.