Four 4s Puzzle and Logarithms

The video explores the Four 4s puzzle, a mathematical challenge where participants use four instances of the number 4 and various mathematical operations to create as many numbers as possible. Initially, basic operations like addition, subtraction, multiplication, and division are used to reach numbers up to 10. Advanced techniques such as concatenation, factorials, and square roots are introduced to reach higher numbers. The video demonstrates how logarithms can extend the puzzle to infinity, providing a proof for this claim. Historical context is provided, highlighting the puzzle's popularity and Paul Dirac's contribution to solving it.

How can you use four 4s to create the number 0?

• 4 + 4 + 4 + 4

• 4 - 4 + 4 - 4

• 4 * 4 - 4 * 4

• 4 / 4 + 4 / 4

Which operation is introduced to reach numbers up to 20?

• Concatenation

• Trigonometry

• Logarithms

• Exponentiation

What is the factorial of 4?

• 8

• 16

• 24

• 12

What base is used for logarithms to extend the Four 4s puzzle to infinity?

• Base e

• Base 10

• Base 2

• Base 4

What is the log base 4 of 16?

• 4

• 1

• 2

• 3

How can you express half using two 4s?

• 4 * 4

• 4 / 4

• √4 / 4

• 4 - 4

What is the result of log base half of half?

• 3

• 2

• 1

• 0

What mathematical concept did Paul Dirac use to solve the Four 4s puzzle?

• Complex numbers

• Logarithms and square roots

• Calculus

• Trigonometry

In which century did the Four 4s puzzle first become popular?

• 21st century

• 19th century

• 18th century

• 20th century

What is the eccentricity of a parabola?

• 1

• 0

• Infinity

• 2