perplexus.info :: Logic : Lights On Diagonally

Lights On Diagonally (Posted on 2009-07-15)

"Lights Switched" toggles the cell selected and its immediate orthogonal neighbours.
"Lights On Diagonally" does exactly the same except that diagonal neighbours are toggled on or off, ie, if a neighbour is on it is turned off.

Select an "N x N" grid size to display that grid for examination.

Offer a lowest switching sequence for each grid (for the 3 x 3 it takes 5).

Submitted by brianjn

Rating: 4.5000 (2 votes)

Solution: (Hide)

My solution for 3 x 3 and 4 x 4 were as pcbouhid had cited in his comments 1 and 2.

I did not have solutions beyond those and I admit that I was relying upon Charlie to provide avenues for solutions for the other configurations.

In his "Lights Switched" Jer added a comment The search for order... I wonder if, by having both the orthogonal and diagonal switching, a sense of order might now be able to be reached.

It will be apparent that binary, or more precisely mod(2), is significant here.

Under Jer's orthogonal scenarios a corner cell toggles 2 neighbours, other edge cells control 3 while inner cells influence 4. In the diagonal scenario these are corners, 1; edges, 2; and inner, 4.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: to Brian	brianjn	2009-07-16 22:17:06
to Brian	pcbouhid	2009-07-16 14:36:59
re(2): computer solution	Charlie	2009-07-16 01:15:48
re: computer solution	brianjn	2009-07-15 21:06:42
computer solution	Charlie	2009-07-15 19:01:00
solution for 4x4	pcbouhid	2009-07-15 14:55:40
solution for 3x3	pcbouhid	2009-07-15 14:47:58

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