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## Is NP reducible to NP-complete?

A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, **the problem is NP-complete**.

## Is NP-hard always NP-complete?

A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time. NP-**Hard problems are as hard as** NP-Complete problems. NP-Hard Problem need not be in NP class. … A non-deterministic Turing machine can solve NP-Complete problem in polynomial time.

## Is N puzzle NP-complete?

Finding a solution to n-Puzzle with the **fewest number of moves** has been shown to be NP-Complete by Ratner and Warmuth (1990).

## Can NP problems be reduced to NP-hard?

No. Suppose that X is NP-hard and it reduces to Y. By definition of NP-hardness, **every problem in NP reduces to X**. By transitivity of reduction, every problem in NP also reduces to Y, so Y is NP-hard.

## Are NP problems solvable?

The short answer is that **if a problem is in NP, it is indeed solvable**.

## Is NP-hard harder than NP-complete?

The set of NP-hard problems is a superset of the set of NP-complete problems. There are **complexity classes more “difficult” than NP**, for example PSPACE, EXPTIME or EXPSPACE, and all these contain NP-hard but not NP-complete problems. Turing halting problem is undecidable and it belongs to NP-Hard set.

## Why is NP-hard not in NP?

An NP-hard problem **can be beyond NP**. The polynomial-time reduction from your X to any problem in NP does not necessarily have a polynomial-time inverse. If the inverse is harder, then the verification is harder. An NP-complete problem, on the other hand, is one that is NP-hard and itself in NP.

## How many steps does it take to complete Tower of Hanoi if there are 5 disks?

Three is the minimal number of moves needed to move this tower. Maybe you also found in the games three-disks can be finished in seven moves, four-disks in 15 and five-disks in **31**.

## Is Hanoi Tower hard?

The Towers of Hanoi is an ancient puzzle that is a good example of **a challenging or complex task** that prompts students to engage in healthy struggle. … To solve the Towers of Hanoi puzzle, you must move all of the rings from the rod on the left to the rod on the right in the fewest number of moves.

## What is the problem of Tower of Hanoi?

Initially, all the disks are placed on one rod, one over the other in ascending order of size similar to a cone-shaped tower. The objective of this problem is **to move the stack of disks from the initial rod to another rod**, following these rules: A disk cannot be placed on top of a smaller disk.