Level Up - Puzzles: Connect a 4x4 Grid of Dots With 6 Contiguous Lines (5x5 w/8, 6x6 w/10)

(TLDR: After solving a 3x3, try to solve a 4x4, 5x5, etc. I have proof that all of them have a solution.)

A common brain teaser is to connect a 3 by 3 grid of dots with four straight lines without picking up the pencil. See image below:

A 3x3 grid. Connect the dots with four connecting lines.

Now, as more and more people learn how to solve this 3x3 problem everyday, I wanted to try to solve a possibly harder puzzle, a 4x4, and connect those dots with just 6 straight lines. There will be no spoilers today in this post and how to answer it, but it is possible to solve. The puzzle involves more thinking outside-the-box.
A 4x4 grid. Connect each of the dots with 6 contiguous straight lines.

And, after you have figured out the 4x4 grid solution, I recommend trying the 5x5 and 6x6 to see if you can solve those as well. I consider it to be a fun challenge.

A 5x5 grid. Connect each dot by 8 connecting, straight lines.

A 6x6 grid. Connect each dot with 10 straight, connected lines.

And, if you would like to solve even larger N by N boxes, then determine the number of lines to use by the equation: 2*N - 2.

In the next few days, I will put the answers into a new post to show that each puzzle mentioned here is possible. I will also prove that any grid of dots can be completed with 2*N - 2 number of lines where N is the grid size, i.e. NxN, and N > 2.

UPDATE: Dot Grid Solutions

~ Danial Goodwin ~

No comments: