Understanding the 2003 Australian Mathematics Competition Problem

The video tutorial presents a challenging math problem from the 2003 Australian Mathematics Competition, where only 3% of students answered correctly. The problem involves a recursive function, f(n), with given conditions. The instructor demonstrates an approach to solve for f(2003) by identifying a repeating pattern in the function values. The solution involves calculating the number of times 3 is added to 11 to reach 2003, and determining the position in the repeating sequence. The instructor verifies the solution by applying the same process to a known value, ensuring accuracy. The video concludes with an invitation for viewers to engage and a preview of the next topic.

What is the initial condition given for the function f in the problem?

• f(11) = 11

• f(11) = 0

• f(11) = 1

• f(11) = -11

What is the formula used to find f(n+3) in terms of f(n)?

• f(n+3) = f(n) - 1

• f(n+3) = f(n) + 1

• f(n+3) = (f(n) + 1) / (f(n) - 1)

• f(n+3) = (f(n) - 1) / (f(n) + 1)

What is the value of f(14) after applying the formula to f(11)?

• 1/2

• 11

• 5/6

• 2/3

How do you simplify the expression when dealing with fractions within a fraction?

• Subtract the fractions

• Divide the fractions

• Add the fractions

• Multiply top and bottom by the same number

What is the value of f(17) after simplification?

• 11

• -11

• -1/11

• 1/11

What pattern is observed in the function values as n increases?

• The values decrease exponentially

• The values remain constant

• The values form a repeating cycle

• The values increase linearly

How many 3s are added to 11 to reach 2003?

• 664

• 500

• 1000

• 200

What is the significance of the number 64 in the calculation?

• It is a prime number

• It is a multiple of 4

• It is a perfect square

• It is a Fibonacci number

What is the final value of f(2003) based on the pattern?

• 11

• -1/11

• -6/5

• 5/6

What method is used to verify the solution for f(2003)?

• Using a calculator

• Guessing the answer

• Using a computer program

• Repeating the process with another number