What type of problem is Sudoku?

Sudoku is a logic-based puzzle. It is a type of constraint satisfaction problem, where the solver is given a finite number of objects (the numerals 1-9) and a set of conditions stating how the objects must be placed in relation to one another.

Is Sudoku an NP problem?

Introduction. The generalised Sudoku problem is an NP-complete problem which, effectively, requests a Latin square that satisfies some additional constraints. In addition to the standard requirement that each row and column of the Latin square contains each symbol precisely once, Sudoku also demands block constraints.

What kind of math is used in Sudoku?

To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.

What type of intelligence is Sudoku?

Sudoku is an informal practice available outside academia that trains fluid intelligence but not crystallized intelligence. Sudoku is a shortcut for training fluid intelligence that bypasses the necessity for science and math courses which don't appeal to all humans and are unavailable to many.

What is the logic for solving Sudoku puzzles?

The most basic strategy to solve a Sudoku puzzle is to first write down, in each empty cell, all possible entries that will not contradict the One Rule with respect to the given cells. If a cell ends up having only one possible entry, it is a "forced" entry that you should fill in.

Sudoku Problems

Is Sudoku a CSP problem?

Sudoku Example of CSP

All sudoku puzzles can be forumulated as CSP by considering each cell as a variable. The initial domain of all cells is {1,2,3,4,5,6,7,8,9}. The constraints are formulated by the fact that in the solution of a sudoku puzzle, no two cell in a row, column or block can have identical numbers.

Is Sudoku an optimization problem?

Sudoku is a puzzle where the player assigns digits to squares (see Wikipedia for a complete description). The puzzle can be formulated as a mathematical optimization problem and solved in a few milliseconds on a decent laptop.

What is the difference between P and NP Sudoku?

To hopefully review, problems in P are those that can be solved "quickly", or more specifically in a time that is polynomial in the size of the problem. Problems in NP are those that can be checked "quickly", or more specifically, in a time that is polynomial in the size of the problem.

Is Sudoku a high IQ game?

Practising a game like sudoku or using a brain training app might make you better at it but it won't boost your IQ or general brain power, a study claims. And instead, researchers suggest people exercise more, socialise and make sure they get enough sleep if they want their mind to be sharper.

Is Sudoku a permutation or combination?

Sudoku is all about permutations, well permutations with an extra twist of logic. To look into the theory behind Sudoku you need to first look into permutations.

What is the 45 rule in Sudoku?

The 45 rule is a basic solving-technique in Killer Sudoku. Each house (row, column, nonet) must add to 45 (the sum of the digits 1 through 9).

Are you smart if you can solve Sudoku?

From this case study it can be concluded that an individual who is skilled at solving Sudoku puzzles likely has a high general IQ. The results of the weak correlation between Sudoku scores and the WAIT test indicates that in some cases a high Sudoku doesn't necessarily mean a high general IQ.

What is the Sudoku Solver algorithm called?

The simplex algorithm is able to solve proper Sudokus, indicating if the Sudoku is not valid (no solution). If there is more than one solution (non-proper Sudokus) the simplex algorithm will generally yield a solution with fractional amounts of more than one digit in some squares.

Why is Sudoku not actually a math puzzle?

Myth: You must be good at math to play Sudoku

But this is not true. Sudoku is not about adding or subtracting or doing arithmetic – it's about placing numbers 1-9 on a grid, without repeating any of the same numbers within the same row, column or square. Sudoku is not a “math” game, it's a logic game.

What is the problem complexity of Sudoku?

The time complexity for solving sudoku using backtracking is tricky to calculate. The worst case time complexity is equal to the number of possible board configurations which is 9^81. This can be even boiled down to 9^k where k is the number of empty cells in the initial board configuration.

What is the average time to solve a Sudoku?

It can be incredibly challenging to solve a Sudoku puzzle. That's what makes it fun. It is believed that the average Sudoku player spends approximately 20 minutes solving a typical Sudoku puzzle. For very hard puzzles, that number can be much higher.

Is Sudoku good for OCD?

It feeds your OCD tendencies.

Every row, column, and square must have all 9 digits for the puzzle to be solved. The symmetry and the way the game works that makes it appealing to people of all ages. I've been doing sudoku puzzles since I was ten years old and I still do them today.

Does Sudoku fight dementia?

“Just sitting down and doing Sudoku isn't probably going to be the one key thing that's going to prevent you from developing Alzheimer's disease,” she said. Moreover, doing only one type of puzzle or another is not the key either. The brain needs to be exercised, just like any other muscle in the body.

What algorithms solve CSP?

Solving algorithms for CSP has four, which is respectively backtracking (BT), iterative broadening (IB), back jumping (BJ)［3］. These algorithms are used tree structure to represent the current search state, each nodes of tree can be regarded as the partial solution.

Does Sudoku improve logic skills?

Playing sudoku online promotes critical thinking

Educators and researchers have discovered the joys of sudoku not just as a game, but as a testament to active learning. Playing sudoku online trains deductive reasoning skills, which is critical in the development of logical thought processes.

Is there a mathematical formula for Sudoku?

Then the number of ways that C can be completed to a full Sudoku grid can be calculated: call it n_c. We also need the number m_C of first bands that share this number n_C of grid completions. Then the total number of Sudoku grids will just be N=Σ_Cm_Cn_C, or the sum of m_Cn_C over all of the 44 bands.

Does Sudoku train your brain?

Since solving Sudoku involves executive cognitive functions, most importantly problem-solving and decision-making, it can be a promising tool for neurorehabilitation and cognitive remediation therapy in neuropsychiatric disorders.