# Online 5x5 Solver

**Play online with the Professor's Cube with this online 5x5x5 Rubik's Cube simulator. Press the Scramble button to jumble the 5x5x5 Rubik's puzzle then try to solve it using the rotation buttons. **

You can use the same buttons which you already know from the 4x4x4 Rubik's Revenge simulator. Every capital letter marks a face rotation. If you see a small 2 after the letter that means that you turn two faces at the same time. Go ahead and test it.

- Big Boggle Solver or the Boggle 5x5 Solver. Played on the 5x5 grid, this Boggle variant may be just as exciting for Boggle fans as the standard 4x4 version of Boggle. Of course, our Boggle 5x5 Solver crunches all possible answers in milliseconds.
- You will need to get assistance from your school if you are having problems entering the answers into your online assignment. Phone support is available Monday-Friday, 9:00AM-10:00PM ET. You may speak with a member of our customer support team by calling 1-800-876-1799.
- Online Calculator for Determinant 5x5. The online calculator calculates the value of the determinant of a 5x5 matrix with the Laplace expansion in a row or column and the gaussian algorithm.

Inverse Matrix Calculator. Here you can calculate inverse matrix with complex numbers online for free with a very detailed solution. The inverse is calculated using Gauss-Jordan elimination. Read the instructions. Matrix dimension: About the method. To calculate inverse matrix you need to do the following steps. Boggle is a word game where players race to find words hidden in a grid of letters. Enter a Boggle board and see a list of all the words that can be found! Choose a board size - 3x3, 4x4 or 5x5 - and the minimum number of letters each word must have, and get a complete listing of all of the solutions along with point totals and other statistics.

Find out interesting facts and a tutorial on how to solve the 5x5x5 puzzle clicking here.

Have fun!

## Methods explanation

### Laplace Expansion Theorem

The Laplacian development theorem provides a method for calculating the determinant, in which the determinant is developed after a row or column. The dimension is reduced and can be reduced further step by step up to a scalar.

$\mathrm{det\; A}=\sum _{i=1}^{n}{-1}^{i+j}\cdot {a}_{ij}\mathrm{det}{A}_{ij}\text{( Expansion on the j-th column )}$

$\mathrm{det\; A}=\sum _{j=1}^{n}{-1}^{i+j}\cdot {a}_{ij}\mathrm{det}{A}_{ij}\text{( Expansion on the i-th row )}$

where A_{ij}, the sub-matrix of A, which arises when the i-th row and the j-th column are removed.

#### Example of the Laplace expansion according to the first row on a 3x3 Matrix.

$\mathrm{det\; A}=\left|\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right|$

The first element is given by the factor a_{11} and the sub-determinant consisting of the elements with green background.

$\left|\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right|=>{a}_{11}\left|\begin{array}{cc}{a}_{22}& {a}_{23}\\ {a}_{32}& {a}_{33}\end{array}\right|$

The second element is given by the factor a_{12} and the sub-determinant consisting of the elements with green background.

$\left|\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right|=>{a}_{12}\left|\begin{array}{cc}{a}_{21}& {a}_{23}\\ {a}_{31}& {a}_{33}\end{array}\right|$

The third element is given by the factor a_{13} and the sub-determinant consisting of the elements with green background.

## Online 5x5 Solver Games

$\left|\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right|=>{a}_{13}\left|\begin{array}{cc}{a}_{21}& {a}_{22}\\ {a}_{31}& {a}_{32}\end{array}\right|$

With the three elements the determinant can be written as a sum of 2x2 determinants.

## Rubik's Cube 5x5 Solver

$\mathrm{det\; A}=\left|\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right|={a}_{11}\left|\begin{array}{cc}{a}_{22}& {a}_{23}\\ {a}_{32}& {a}_{33}\end{array}\right|-{a}_{12}\left|\begin{array}{cc}{a}_{21}& {a}_{23}\\ {a}_{31}& {a}_{33}\end{array}\right|+{a}_{13}\left|\begin{array}{cc}{a}_{21}& {a}_{22}\\ {a}_{31}& {a}_{32}\end{array}\right|$

## 5x5 Cube Solver

It is important to consider that the sign of the elements alternate in the following manner.

## Magisches Quadrat 5x5 Online Solver

$\left|\begin{array}{ccc}+& -& +\\ -& +& -\\ +& -& +\end{array}\right|$