Recursive Solutions and Mathematical Problems

What is one of the primary issues with a recursive solution?

• It is impossible to solve small problems.

• It cannot refer to previous steps.

• It becomes hard to solve relatively large problems.

• It does not allow for analytical solutions.

Which of the following is an example of a closed-form expression?

• An infinite summation series

• A mathematical equation expressed with a finite number of elementary operations

• A formula requiring iterative computation

• A recursive algorithm

What is NOT an example of an elementary function used in a closed form?

• Exponentials

• Roots of polynomials

• Infinite loops

• Logarithms

Which step is NOT part of solving a problem involving recurrence relations?

• Looking at small cases

• Writing the program first

• Finding and proving a recurrence relation

• Proving the closed form using induction

Which mathematical problem involves moving disks between pegs?

• The Josephus Problem

• The Tower of Hanoi

• The Lines in the Plane

• Fermat's Last Theorem

In the Tower of Hanoi problem, which condition must always be met?

• Disks can only be moved two at a time.

• Smaller disks cannot be placed on larger disks.

• Larger disks cannot be placed on smaller disks.

• Only one disk can be moved at a time.

Who invented the Tower of Hanoi problem?

• Edouard Lucas

• Blaise Pascal

• Carl Friedrich Gauss

• Alan Turing

The Josephus problem involves:

• Transferring disks between pegs

• Arranging lines in a plane

• Eliminating every nth person in a circle

• Finding closed-form solutions

What method is commonly used to prove the closed form of a recurrence relation?

• Mathematical induction

• Empirical testing

• Simulation modeling

• Numerical approximation

The Lines in the Plane problem primarily studies:

• Arranging objects in stacks

• Elimination sequences in a game

• The maximum number of intersections of lines

• Recursive methods for transferring disks