Making any integer with four 2s
The article presents a mathematical puzzle using four instances of the digit 2 to create any natural number, exploring various operations and concepts suitable for different educational levels.
Read original article
The article discusses a mathematical puzzle involving the use of exactly four instances of the digit 2 to create any target natural number through various mathematical operations. It provides examples suitable for different educational levels, starting with simple equations for elementary school students, such as 1, 2, 3, 4, 5, and 6. As the complexity increases, middle school students can explore exponents and factorials to achieve higher numbers like 18, 28, 256, and 65536. The article also highlights creative approaches to reach numbers like 7 using advanced mathematical concepts, including the Gamma function and complex numbers. It notes that while mathematicians in the 1920s enjoyed this puzzle, Paul Dirac later discovered a general solution involving nested square roots. The article concludes by presenting a formula that allows for the expression of any number using four 2s, emphasizing the challenge of visualizing the necessary square roots. The author credits Graham Farmelo's book about Paul Dirac for inspiration and invites readers to share their thoughts via email.
- The puzzle involves using four 2s to create any natural number.
- Examples range from simple calculations for children to complex mathematical concepts for advanced learners.
- The use of the Gamma function and complex numbers allows for creative solutions.
- Paul Dirac's discovery of a general solution simplified the puzzle.
- The article encourages exploration of mathematical creativity and problem-solving.
Related
What is the longest known sequence that repeats in Pi? (homelab)
The article explores repeating sequences in Pi's decimal representation, detailing the transition from Python to C for efficiency, successful identification of sequences, and plans for further extensive searches.
Memorizing the first 100 perfect squares (2022)
The article outlines techniques for memorizing the first 100 perfect squares, emphasizing patterns and tricks over brute force memorization to aid mental calculations and recognize square numbers efficiently.
How to Compose Math Problems
The article highlights how composing math problems fosters creativity and critical thinking, emphasizing characteristics of "beautiful" problems and the importance of pattern recognition in problem formulation and discovery.
Mathematicians Uncover a New Way to Count Prime Numbers
Mathematicians Ben Green and Mehtaab Sawhney proved there are infinitely many prime numbers of the form p² + 4q², utilizing the Gowers norm and building on previous conjectures in number theory.
A Puzzle about a Calculator
Katie Steckles discusses her first year managing the BrainTwisters column, presenting a puzzle about forming four-digit numbers from a calculator keypad, all of which are divisible by 11.
- Some commenters express concerns about the use of functions and operations that may obscure the challenge of using only four instances of the digit 2.
- There is a discussion about the historical context of similar puzzles, such as the "four fours" problem, and references to notable mathematicians.
- Several users share their own solutions and methods, highlighting creativity in approaching the puzzle.
- Critiques arise regarding the clarity and simplicity of certain expressions used in the solutions.
- Some participants suggest that the puzzle could be more engaging with different digits or more complex numbers.
1 commentsRelated
What is the longest known sequence that repeats in Pi? (homelab)
The article explores repeating sequences in Pi's decimal representation, detailing the transition from Python to C for efficiency, successful identification of sequences, and plans for further extensive searches.
Memorizing the first 100 perfect squares (2022)
The article outlines techniques for memorizing the first 100 perfect squares, emphasizing patterns and tricks over brute force memorization to aid mental calculations and recognize square numbers efficiently.
How to Compose Math Problems
The article highlights how composing math problems fosters creativity and critical thinking, emphasizing characteristics of "beautiful" problems and the importance of pattern recognition in problem formulation and discovery.
Mathematicians Uncover a New Way to Count Prime Numbers
Mathematicians Ben Green and Mehtaab Sawhney proved there are infinitely many prime numbers of the form p² + 4q², utilizing the Gowers norm and building on previous conjectures in number theory.
A Puzzle about a Calculator
Katie Steckles discusses her first year managing the BrainTwisters column, presenting a puzzle about forming four-digit numbers from a calculator keypad, all of which are divisible by 11.