A system of linear equations
Solving the (3 times 3) version of Lights Out amounts tosolving the system (Ax=b) over (GF(2)) where(A = begin{bmatrix}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 end{bmatrix})and (b = begin{bmatrix}b_1 b_2 b_3 b_4 b_5 b_6 b_7 b_8 b_9 end{bmatrix}).
- Navigate the list of programs until you find Lights-Out 2 Client or simply click the Search feature and type in 'Lights-Out 2 Client'. If it exists on your system the Lights-Out 2 Client program will be found automatically. When you click Lights-Out 2 Client in the list, some data regarding the application is made available to you.
- How to uninstall Lights-Out 2 for Windows Version 2.0.3.3562 by AxoNet Software GmbH? Learn how to remove Lights-Out 2 for Windows Version 2.0.3.3562 from your computer.
- Lights Out 3.2.0. Expands the functionality of Energy Saver. Version 3.2.0: Note: Now requires OS X 10.7 or later running on a 64-bit Intel processor.
- Navigate the list of programs until you find Lights-Out 2 Client or simply click the Search feature and type in 'Lights-Out 2 Client'. If it exists on your system the Lights-Out 2 Client program will be found automatically. When you click Lights-Out 2 Client in the list, some data regarding the.
Recall that column (i) of (A) represents the action of pressing square (i); the entries in the column equal to 1 correspondto the squares that are toggled when square (i) is pressed.
Source: Hewlett-Packard Company, HP Software Security Response Team VULNERABILITY SUMMARY A potential security vulnerability has been identified in HP Integrated Lights-Out 2, 3, and 4 (iLO2, iLO3, iLO4). The vulnerability could be exploited to allow an attacker to gain unauthorized privileges and unauthorized access to privileged information.
The tuple (b) represents the configuration of lights.Hence, (b_i = 1) if and only if the light at square (i) is on.
Lights Out 3 2 0 2 Bike Hitch Rack
Rider 2019 2020 academic calendar. The variable (x_i) corresponds to square (i) and is set to 0 or 1.It is set to 1 if and only if the corresponding square needs to be pressedin a solution of the game.
We now solve the system using row reduction. The following table shows the entire process.Separating lines have been added to the matricesto aid reading.
begin{align*}~ & left[scriptsizebegin{array}{ccc|ccc|ccc|c}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_1 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & b_2 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & b_3 hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{R_2 leftarrow R_2 + R_1}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_1 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & b_1+b_2 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & b_3 hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{R_1 leftarrow R_1 + R_4}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & b_1+b_2 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & b_3 hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_3 leftarrow R_3 + R_1 R_5 leftarrow R_5 + R_1end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & b_1+b_2 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & b_1+b_3+b_4 hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & b_1+b_4+b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_2 leftarrow R_2 + R_3 R_6 leftarrow R_6 + R_3end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & b_2+b_3+b_4 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & b_1+b_3+b_4 hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & b_1+b_4+b_5 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_2 leftarrow R_2 + R_7 R_4 leftarrow R_4 + R_7 R_5 leftarrow R_5 + R_7end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & b_2+b_3+b_4+b_7 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & b_1+b_3+b_4 hline1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & b_4+b_7 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_1 leftarrow R_1 + R_8 R_3 leftarrow R_3 + R_8 R_4 leftarrow R_4 + R_8end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & b_2+b_3+b_4+b_7 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & b_1+b_3+b_4+b_8 hline1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_4+b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c} R_2 leftarrow R_2 + R_5 R_3 leftarrow R_3 + R_5 R_9 leftarrow R_9 + R_5end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & b_3+b_5+b_7+b_8 hline1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_4+b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_5+b_7+b_9end{array}right] xrightarrow{scriptsizebegin{array}{c} R_4 leftarrow R_4 + R_6 R_7 leftarrow R_7 + R_6R_8 leftarrow R_8 + R_6end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & b_3+b_5+b_7+b_8 hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6++b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & b_1+b_3+b_4+b_6+b_7 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & b_1+b_3+b_4+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_5+b_7+b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_1 leftarrow R_1 + R_9 R_3 leftarrow R_3 + R_9 R_7 leftarrow R_7 + R_9end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_5+b_7+b_8+b_9 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_4+b_8+b_9 hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6++b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_3+b_5+b_6+b_9 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & b_1+b_3+b_4+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_5+b_7+b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_8 leftarrow R_8 + R_2 R_9 leftarrow R_9 + R_2end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_5+b_7+b_8+b_9 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_4+b_8+b_9 hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6++b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6 hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_3+b_5+b_6+b_9 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & b_2+b_4+b_5+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & b_2+b_3+b_4+b_7+b_9end{array}right] xrightarrow{R_6 leftarrow R_6 + R_9}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_5+b_7+b_8+b_9 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_4+b_8+b_9 hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6+b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & b_1+b_2+b_6+b_7+b_9 hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_3+b_5+b_6+b_9 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & b_2+b_4+b_5+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & b_2+b_3+b_4+b_7+b_9end{array}right]end{align*}From the final augmented matrix, we see that(begin{bmatrix}x_1x_2x_3x_4x_5x_6x_7x_8x_9end{bmatrix}=begin{bmatrix}b_1+b_3+b_6+b_7+b_8 b_5+b_7+b_8+b_9 b_1+b_3+b_4+b_8+b_9 b_3+b_5+b_6+b_9 b_2+b_4+b_5+b_6+b_8 b_1+b_4+b_5+b_7 b_1+b_2+b_6+b_7+b_9 b_1+b_2+b_3+b_5 b_2+b_3+b_4+b_7+b_9 end{bmatrix}.)
Lights Out 3 2 0 2 Piece Hardside Set
Hence, if the top-left square is the only one with the light on, thenthe solution is to press squares 1, 3, 6, 7, and 8. (Why?)
Exercises
Solve the (4 times 4) version of Lights Outcompletely. Is there a solution for every possible configuration of lights? Explain your answer. Posterino 3 4 4 cylinder.