i'm going to rephrase lance's question here, b/c i find this to be quite an interesting question, but i want to know if it's even possible?
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
is it possible to end up where you started?
2006-10-19 13:39:12 · 5 answers · asked by Elan G 1 in Science & Mathematics ➔ Mathematics
Yes it is possible!
I tried numerous combinations and the best I got was a star shape through 11 of the 12 dots. Or lines that didn't connect. It took some perseverance, but I finally figured it out!
Give me a second to draw it up...
Edit: I've scanned it and attached it below:
2006-10-19 14:12:57 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
It is possible to traverse the points with a closed network with 5 lines BUT impossible to end up where you started from as a traversible network has to have all even nodes (ie an even number of lines entering/leaving vertices) or exactly 2 odd nodes.
With 5 lines you cannot have a network with all even nodes but you can have one with 2 odd nodes and 2 even nodes
Therefore it would be traversible BUT not have the same start and finish points.
Whoops sorry I am incorrect ..just saw above answer by Puzzling!!!!!
2006-10-19 21:55:41 · answer #2 · answered by Wal C 6 · 0⤊ 0⤋
Most people try to go through the centers, but representing them as circles and describing them as dots allows another solution. The first line goes up and slightly canted to the right, passing through the first three. Second line goes downward and slightly to the right passing through the next column, upward and slightly to the right through the third column, downward and to the right through the fourth column, and straight back to where you began. There may be a way to do it going through the centers, but that wasn't a condition of the problem.
2006-10-19 20:54:17 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Yes - but you have to 'think outside the box'
drawing the lines longer than needed, then returning to cover the missing o's.
it can be done.
2006-10-19 20:43:51 · answer #4 · answered by Anonymous · 1⤊ 0⤋
Oh My GOD!
thank you SO Much!
i would rate ur answer, but seeing as im only a level 1, i cant.
man, u relly helped me out...
how did you know how to do it?
2006-10-19 21:18:18 · answer #5 · answered by Lance K, Texas 1 · 0⤊ 0⤋