Is there any easy way to solve this lock puzzle?

Question

https://js13kgames.com/games/lock-puzzle/index.html

The link provides an online puzzle game of $16$ tiles in the form of a $4 times 4$ matrix of which some entries are in the form of vertical tiles and other in the form of horizontal tiles arranged randomly by the system. Once you press a tile the tile along with all the tiles with same rows and columns get reversed i.e. vertical tiles becomes horizontal and vice versa. In order to solve it all we have to do is to make each of the $16$ tiles vertical.

I have solved it yesterday taking about half an hour. But I don't remember all the methods I used. My question is "Is there any algorithmic way of solving this puzzle which needs small amount of time"?

Jaap Scherphuis · Accepted Answer

There is an easy way to solve it in the minimum number of moves.

The reason this works is:

JMP · Answer

Or, create a new blank board, and click on it all the positions of the 'on' switches from the original board. Take this new pattern back to the original board, and click every 'off' position from the new board onto the original board. All lights are on!

Answered by JMP on September 26, 2021

hdsdv · Answer

I don't know why this works, but I tried my old strategy from other similar puzzles and it has worked in several cases so far:

Then,

One final note - since I don't know why it works, I also can't prove that it always works, unfortunately. But in my many years of solving puzzles in this genre, that strategy always seems to eventually land on a solution.

Edit: See Jaap Scherphuis's comment and answer for an explanation of why this works.

Is there any easy way to solve this lock puzzle?

3 Answers

Add your own answers!

Ask a Question