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 Lights Out! (2) (Posted on 2022-10-31)
Imagine there is a 7x7 grid of lights, and only the middle in the grid is on.

The lights are wired such that when you flip the switch for one light (from on to off or off to on) the others next to it (not diagonally) flip as well.

Using this weird wiring of lights, what is the fewest number of switch changes it takes to turn all the lights off, and which lights should you switch?

Note: Assume all the switches work in the manner explained, and there is one switch for each of the lights.

 See The Solution Submitted by K Sengupta Rating: 5.0000 (1 votes)

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 computer solution | Comment 1 of 24
clearvars,clc
global rowChoice lights switches highrow
rowChoice={};
for k=0:7
c=nchoosek(2:8,k);
for i=1:size(c,1);
rowChoice{end+1}=c(i,:);
end
end
rowChoice;

lights=zeros(9,9); lights(5,5)=1;
switches=zeros(9,9);

highrow=0;

addon(2); % row and column numbers are 1 higher to provide a surrounding buffer

highrow

global rowChoice lights switches highrow
if row>highrow   % highrow was for debugging
highrow=row;
end
for i=1:length(rowChoice)
saveLights=lights; saveSwitches=switches;

w=rowChoice{i};
switches(row,:)=0;
for j=1:length(w)

switches(row,w(j))=1;
for c=w(j)-1:2:w(j)+1
lights(row,c)=xor(lights(row,c),1);
end
for r=row-1:row+1
lights(r,w(j))=xor(lights(r,w(j)),1);
end
end

if row>2
if ~isequal(lights(row-1,2:8),zeros(1,7))
lights=saveLights; switches=saveSwitches;
continue
end
end
if row==8

if ~isequal(lights(row,2:8),zeros(1,7))
lights=saveLights; switches=saveSwitches;
continue
end

disp(switches(2:8,2:8))
disp(' ')

disp(lights(2:8,2:8))
disp(' ')
disp(sum(switches(2:8,2:8),'all'))
disp(' ')
else
end

lights=saveLights; switches=saveSwitches;
end
end

finds

` 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     17`

showing the 17 flipped switches on top and a confirmation of all the lights off below that.

 Posted by Charlie on 2022-10-31 10:31:43

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