Naughts and Crosses - Puzzle 2

[jowoodhouse]

I know this is from the archive, so maybe someone has already posted this but anyway, I have an alternative solution:

The puzzle is: What is the fewest number of lines needed to connect all nine dots in the image to the left, without lifting your pencil, or folding your monitor (not recommended)? (The picture shows a square of 9 dots, 3 per row, 3 rows across and 3 rows down)

Anyway, my solution is: 1. The question does not state that the line(s) must be straight. A curved, 's'-shaped line could join the lot!

[groza528]

line n.
Mathematics. A geometric figure formed by a point moving along a fixed direction and the reverse direction.
Lines can't curve. If they curved, they wouldn't be lines anymore, they'd be curves.

[groza528]

technically the given answer isn't correct either in that case. If you aren't allowed to lift your pencil, you'll never finish drawing your line, and you can't continue to the next dot. Can we get somebody to change that to 'line segments?'

[BearTalon]

Whether or not you lift your pencil is irrelevant.

In order to join all 9 dots in a 3 X 3 pattern, you need a minimum of 4 lines. For example, 3 horizontal parallels going through all 9 dots, and one vertical through three dots.

The part about not lifting your pencil is just the mechanics of the puzzle to NOT have simple solutions like the ones I mentioned above.

Third, common usage of the word line refers to any mark between two points, whether curved or not - the lines of a car; "color inside the lines". Yes, lines in mathematics are straight and infinite in length, but we ALL refer to segments as lines, without needing to elaborate or knowing that the mathematical version of line is different.

[CrystyB]

The Solution states (to the best of my knowledge) that the basic elements of the puzzle are not accurate math entities, but a rather loose acceptance of them. It's a mind-bending puzzle, not a math problem!

PS I also forgot to say that the actual GL solution is 3 (three) lines, without lifting the pencil off the paper. For instance that comb of three lines united at one edge is not obtainable like that - it has 4 points of odd order and that requires 2 pencil passes.

[This message has been edited by CrystyB (edited 03-16-2002 08:52 PM).]

[soda sipper]

What about a really fat line? If I had a big enough pen, I could just connect all the dots with one really thick line.