Dot puzzle

[nibble4bits]

Using only 4 lines, and not picking your pencil up, could you cross all 9 of these dots if this was printed?

Are there methods to go lower? How low can you go?

[mfgoode]

Nibble4bits this has come up before if my memory serves me right so I wont spoil your problem even by spoilerising the answer.
What do you mean by going low? you can even go higher depending where you start.
Mally

[fetofs]

I love this solution!

[fetofs]

Seriously speaking...

[mfgoode]

Originally Posted by fetofs

I love this solution!

Mally

[Fusion_power]

Fetofs was being facetious.

[Orgasmic Troll]

I think we've discussed this one before

as long as the dots (or the width of the pencil mark) cannot be taken arbitrarily small and the paper we write on CAN be taken arbitrarily large, the solution is 3 lines

[mfgoode]

:surprised Three straight lines TravisT ? I'd like to see your solution.
Please oblige.
Mally

[xilman]

Originally Posted by mfgoode

:surprised Three straight lines TravisT ? I'd like to see your solution.
Please oblige.
Mally

If the line is wide enough, at least as wide as the diagram, a single line suffices even for zero-sized dots.

If the dots are large enough, of diameter at least as wide as the diagram, a single line suffices, even if it is of zero width.


Paul

[mfgoode]

Originally Posted by xilman

If the line is wide enough, at least as wide as the diagram, a single line suffices even for zero-sized dots.

If the dots are large enough, of diameter at least as wide as the diagram, a single line suffices, even if it is of zero width.


Paul

Your two "IF"'s reminds me of the saying "IF stands stiff in 24 corners"
Your "IF" s offends my mathematical classical sense.!
Lets not bend the rules of the game and stick to the definitions of Euclid which has stood good for over two millenniums. I reiterate

Line: has only length and no breadth.

Point: that which has position and no dimensions.

It would be better if you used a single curved line which is not restricted in the problem instead of using quadrilaterals and circles.
Mally

[Orgasmic Troll]

Line: has only length and no breadth.

Point: that which has position and no dimensions.

There are no points in this problem. They are dots. Specifically, the problem states that they are printed, therefore, they have a minimum radius r

thus imagine a rectangle of width r that is just large enough to cover the top row of 3 dots. Draw a line that passes through one corner to the other, since it has non-zero width, the line is not parallel to a line through the centers of the dots and thus will intersect the line that bisects the 2nd row. Create a new line through the bottom row by translating the first line down. Similar to the original line, this will also intersect the middle line, thus we have 3 lines that intersect all 9 dots