Hard Problem-for senior math prob.?

Question

if i have, on paper, a diagram consisting of 3 rows of 4 dots; starting wherever i want on the paper, not taking the pencil off the paper, and only using 5 straight lines, how can i cross out all 12 dots, while ending up where i began?

the diagram looks like this:

0 0 0 0
0 0 0 0
0 0 0 0

Answer 1

Oops, I didn't see the part about *ending where I began*. That's critical.

It's very easy to draw 5 connected lines (go through the top row, down one, through the second row, down one, through the last row = 5 lines.)

But it is much tougher to find a way to connect the lines back to where you started.

It took some working, but I finally figured out a solution. I drew it up and scanned it. It's attached below.

Answer 2

ok, so just to make my explantation easier, label each dot 1-12 going left to right, top to bottom, so topw left is 1, bottom right is 12.

Start at 1, draw down crossing out 5 and 9, keep drawing down a little further

from this point draw up and right at 45º to the vertical ccrossing out 10, 7 and 4, stop at 4

draw left corssing out 3 then 2, bring the line back to 1

now draw down and right at 45º to the horizontal crossing off 6 and 11, keep going till you are below the last column of numbers

draw up crossing off 12 and 8, and there you have it, all dots crossed off in 5 straight lines. Cool huh?

Answer 3

start bottom left corner, draw horizontal line movin towards the right through all dots,1, then draw a line to the next row,2, draw a line through all that row all the way to the left,3, draw a line up 1 line to the next row ,4, draw a line to the right all the way gettin the last line,5,
the hard one is same problem but 4 lines and 3x3
o srry, didnt c u havta finish where u started, good luk

Answer 4

Oh wowl i dont think it is possible to end up where you started?

i like the previous answers, but where did you get this question from? are you sure it's possible?

i just rephrased your question, as it seems ppl dont see the "end up where you started part"

Answer 5

this must be a variant of the 3X3 formation...i'm stumped

he needs to End up where he started ppl!

is this possible?