# X's and O's puzzler

• Sep 21st 2005, 06:14 PM
ianlv
hard hw problem :(
My high school geometry teacher gave me this today and is asking if it is possible. I really need the extra credit so someone plz help.

X X X

O O O

Can you connect each X to each O without crossing over any lines. You may go in any direction from the x to the designated 0, including over x's and under x's(as long as they line does not over lap another line.) plz show any equations u used to solve problem if theres a solution.
• Sep 21st 2005, 06:29 PM
MathGuru
One possible solution
Fold up the page so that every x and every o are stacked one on top of the other. Now stab a pencil through the paper and you are done.
• Sep 21st 2005, 06:31 PM
MathGuru
Another possible solution
Roll up the paper so that it makes a tube, now draw one straight line starting at the bottom right o and towards the top right x but at an overall slant so that when it somes around the loop it hits the middle o and middle x and so on.

Now you have one line that passes through all x's and o's
• Sep 21st 2005, 06:36 PM
ianlv
ty a lot
• Sep 21st 2005, 06:46 PM
bluedragon25
math question 101
ianlv quoted: My high school geometry teacher gave me this today and is asking if it is possible. I really need the extra credit so someone plz help.

X X X

O O O

Can you connect each X to each O without crossing over any lines. You may go in any direction from the x to the designated 0, including over x's and under x's(as long as they line does not over lap another line.) plz show any equations u used to solve problem if theres a solution.

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i beleive this answer is however possible as it was completed by Albert Einstein, however i dont know the solution. I recall this question back in high school and do beleive its possible with just drawing lines on an unfolded sheet of paper if anybody has that solution it would be greatly appreciated.
• Sep 21st 2005, 10:47 PM
hoeltgman
No there isn't a solution to this I believe. Even Einstein cheated on that question. He then draw one line under another. As far as I know there isn't any solution. At least I have never seen one.
• Sep 21st 2005, 11:28 PM
ticbol
No crossing/overlapping of lines. Okay.
If one arrow head, or one end-of-line, touches a circle, that line connets to the circle.
The 3 circles shown are not dots---they have holes or empty interiors. [ :-) ]

"Connect each x to each O"
That does not say "draw 3 lines from an x, and end one line each to the 3 circles." [ :-) ]

Solution:

From the left x, draw only one line, and touch/connect it counterclockwise (or from left to right) to the bottoms of the 3 circles.

From the middle x, draw only one line and let it pass through--at the centers/middles-- of the 3 circles from left to right.

From the right x, draw only one line and let it touch/connect, from left to right, the tops of the 3 circles.

Of course, make sure the 3 lines don't touch while you draw them.

My "one line" does not mean one straight line. My "one line" here means any line---straight, crooked, curved, whatever, but not fully straight.

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That is one solution.

Reverse the direction of touching/connecting. Do it all from right to left this time. Right x to bottoms. Middle x through the centers. Left x to tops.
Another solution.

From the left and middle x's, connect left to right. (Left x to bottoms; middle x through centers.) From the right x, connect to tops right to left.
Third solution.

..
...etc

More than 3 solutions actually.
• Sep 22nd 2005, 12:41 AM
hoeltgman
Ok that way it works. I had a teacher that gave us this problem too and he told us that there isn't any solution if we are supposed to connect each point with each x with separate lines. And that all the lines must be in one plane. Under theses circumstances he told us it would be impossible to make it.