A 10,958 Solution - Numberphile
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, he attempts a complex calculation involving multiplication, division, and addition, which results in 10,958.4, just shy of the target. He then discusses the overlooked use of concatenation in mathematical operations and successfully finds a more precise solution: concatenating 1 with 2, then multiplying by 3 and adding 8, followed by multiplying by 9, which accurately reaches 10,958. The video highlights the importance of embracing the challenge and trying unconventional methods, even when they seem unlikely to succeed.
Takeaways
- 🔢 The video discusses a mathematical challenge to get as close as possible to the number 10,958 using basic arithmetic operations and concatenation.
- ✂️ The rules allow for addition, subtraction, multiplication, division, and the use of brackets to dictate order of operations, but powers are not used due to computational complexity.
- 🔣 Concatenation is permitted in the challenge, which means combining numbers in sequence without arithmetic operations, and it's an aspect that's not always explicitly stated but utilized in the challenge.
- 🎲 The presenter attempts to solve the challenge by creating an expression using the numbers 1 through 9 with concatenation and arithmetic operations, aiming for the number 10,958.
- 📉 In the initial attempt, the presenter gets close but not exact, resulting in 10,958.4 instead of the desired 10,958.
- 📌 The presenter emphasizes the importance of trying out solutions even if they might fail, as it can lead to finding a correct solution in the end.
- 🤔 The video highlights the arbitrary nature of including concatenation in mathematical operations and how it's not typically used as a step in calculations but rather in setting up numbers.
- 📝 The presenter corrects the initial approach by rearranging the concatenation and arithmetic operations to precisely hit the target number 10,958.
- 🎯 The final expression provided is a combination of concatenation and arithmetic that successfully reaches the goal of 10,958, filling the gap left by previous attempts.
- 💡 The video serves as a lesson in creativity and perseverance in problem-solving, showing that sometimes thinking outside the box and trying unconventional methods can lead to success.
- 👕 There's a humorous mention of Parker Square t-shirts, indicating a level of community and following around the presenter's mathematical content.
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 the order of operations. Powers are allowed but not used in this specific instance due to the complexity they add to programming.
Why were powers not used in the solution presented in the video?
-Powers were not used in the solution because when writing a program to perform the calculations, they can cause the values to become extremely large, leading to computational issues. It was easier to avoid them in this case.
What is concatenation in the context of the video?
-In the context of the video, concatenation refers to the process of joining two sequences of numbers together to form a new sequence. It is a mathematical operation that is allowed but not explicitly stated in the rules.
What symbol does the video suggest using to represent concatenation?
-The video suggests using two lines ('//') to represent concatenation, although it acknowledges that there are various symbols people use for this purpose.
What was the initial attempt at the solution and how close did it get to the target number 10,958?
-The initial attempt involved a series of mathematical operations including concatenation, multiplication, division, and addition. The result was 10,958.4, which was very close to the target number of 10,958.
What is the significance of the number 10,958 in the video?
-The number 10,958 is the target number that the presenter is trying to reach using the allowed mathematical operations and concatenation.
What is the final solution presented in the video to reach the number 10,958?
-The final solution involves concatenating numbers, performing multiplication and addition operations, and using brackets to dictate the order of operations. The sequence is 1 concatenated with 2, multiplied by 3, multiplied by 4, divided by 5, multiplied by 6, multiplied by 7, plus 8, all within brackets, and then multiplied by 9.
Why was concatenation not used as a step during the calculation in the initial examples?
-Concatenation was not used as a step during the calculation in the initial examples because it was only used in the setup of the numbers, which were then subjected to other operations.
What is the moral of the Parker Square challenge as presented in the video?
-The moral of the Parker Square challenge is to give it a try even when the odds of success are low. Embracing failure is part of the process, and sometimes it does work out.
How does the presenter suggest improving the understanding of the problem?
-The presenter suggests that taking concatenation seriously and including it as a fully-fledged function in the calculations can help improve the understanding and potentially solve the problem.
What is the role of the base in the context of the video's mathematical discussion?
-The base is mentioned in the context of logarithms, suggesting that the base of a logarithm could be used to determine the length or another property of a number in the sequence.
Outlines
🔢 Mathematical Operations and Concatenation
The script discusses the rules of a mathematical challenge that allows addition, subtraction, multiplication, division, and the use of brackets to dictate order of operations. However, the use of powers is discouraged due to the potential for large values when programming. The concept of concatenation is introduced, which is the joining of numbers without any mathematical operation, and it's noted that there's no standard symbol for it. The speaker uses a double line to denote concatenation and provides an example calculation that nearly achieves a target number, 10958, by concatenating and then performing operations on the numbers 1 through 7, and finally multiplying by 9.
🔄 Embracing Concatenation in Mathematical Puzzles
This paragraph delves deeper into the use of concatenation in the context of the mathematical challenge. The speaker points out that while concatenation is not explicitly forbidden, it's also not used as a step in calculations but rather in setting up numbers for operations. The script then presents a revised calculation that correctly achieves the target number, 10958, by concatenating numbers and performing operations in a sequence that includes multiplication, addition, and finally multiplication by 9. The speaker emphasizes the importance of trying out methods that might seem unlikely to succeed, as they can occasionally lead to the correct solution.
Mindmap
Keywords
💡Concatenation
💡Arithmetic Operations
💡Brackets
💡Powers
💡Parker Square
💡T-shirt
💡Logarithm
💡Explode
💡Rules
💡Sequence
💡Moral
Highlights
The video discusses the challenge of getting as close as possible to the number 10,958 using basic mathematical operations and concatenation.
Powers are allowed but not used in the solution to avoid large values when programming.
Brackets are utilized to determine the order of operations.
Concatenation is a less commonly used operation in the challenge, symbolized by two lines.
The video explores the concept of concatenation and its various notations.
An initial attempt to reach the target number results in 10,958.4, which is very close.
The presenter's approach involves starting with the number 12 and applying a series of mathematical operations.
The use of concatenation is not explicitly stated but is implied and utilized in the solution.
A successful solution is found by taking concatenation seriously and using it in the calculation steps.
The final solution reaches the exact target number of 10,958 by concatenating numbers and applying mathematical operations.
The presenter emphasizes the importance of trying even if the odds of success are low.
The video concludes by encouraging viewers to embrace failure as part of the problem-solving process.
The mathematical process involves adding, subtracting, multiplying, dividing, and concatenating numbers.
The presenter demonstrates a step-by-step approach to the problem, including the use of brackets and concatenation.
The video highlights the arbitrary nature of including concatenation as a function in the problem-solving process.
The presenter shares a moral lesson from the Parker square, encouraging viewers to give problems a try despite the potential for failure.
The video showcases the beauty of mathematics in finding creative solutions to complex problems.
The final solution is achieved by concatenating numbers in a specific order and performing calculations.