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martin gran
guest

Sep1302, 01:06 AM (EST) 

"drawing puzzle"

My third grade math teacher gave us a drawing puzzle I'm still trying to solve thirty odd years later. Now my daughter's trying to figure it out and I don't want her wasting as many hours on this as I did. The first excercise is to draw something that looks like a house with an "X" in the bottom square without lifting the pen or doubledrawing a line. That's easy enough. The next step is to add the triangular rooflike thing on each of the 4 sides of the box with the "X" in it. That I can't seem to do (within the rules above). Nor can I figure out why it's impossible. Is this a popular puzzle? Can anyone out there help me solve it before my daughter throws away the best years of her life trying to solve it? Thanks. martinrgran@earthlink.net 

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alexb
Charter Member
2673 posts 
Sep1402, 02:28 AM (EST) 

1. "RE: drawing puzzle"
In response to message #0

>My third grade math teacher gave us a drawing puzzle I'm >still trying to solve thirty odd years later. Now my >daughter's trying to figure it out and I don't want her >wasting as many hours on this as I did. May she be more gifted? May she enjoy solving problems or this puzzle in particular? May it be useful to sometimes use one's brain? > >The first excercise is to draw something that looks like a >house with an "X" in the bottom square without lifting the >pen or doubledrawing a line. That's easy enough. > >The next step is to add the triangular rooflike thing on >each of the 4 sides of the box with the "X" in it. That I >can't seem to do (within the rules above). Nor can I figure >out why it's impossible. Search the Web or this site for "Euler path" or "Unicursal Drawings". >Is this a popular puzzle? Very much so. >Can anyone out there help me >solve it before my daughter throws away the best years of >her life trying to solve it? May she waste the best years of her life without trying to solve it?


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Soroban
Member since Sep1002

Sep1802, 05:36 PM (EST) 

3. "RE: drawing puzzle"
In response to message #1

>>Can anyone out there help me >>solve it before my daughter throws away the best years of >>her life trying to solve it? > >May she waste the best years of her life without trying to >solve it? I agree, Alex ~ yet sending her on a yearslong futile search (for a solution for a problem known to have no solution) could be considered a "waste". I believe it was the Star Trek episode "Wolf in the Fold" in which Spock ordered the possessed computer to calculate the exact value of pi ~ thus occupying the computer so thoroughly that our heroes could save the crew, the Enterprise, the United Federation of Planets, and Life As We Know It. ~~~~~~~~~~ An "even" vertex is one which has an even number of line segments emanting from it. The center of the X has 4 segments; it is even. The peak of a "roof" has 2 segments; it is even. Elementary graph theory states: a figure is "traversable" if (1) all vertices are even, or (2) there are no more than two odd vertices. Consider: When you pass through a point, you have made it an even vertex ~ one path in, one path out. A vertex is odd if (1) you start at that vertex, or (2) you end at that vertex. (It may take some sketching to understand these statements.) If there is one odd vertex, we must start at that vertex. And the rest of the figure (all even) can be traversed. If there are two odd vertices, we must start at one of them and end at the other. With more than two odd vertices, the traversing is impossible. (And the given problem has four odd vertices.) (Naturally, someone is bound to suggest folding the paper, or drawing the figure on a torus, etc. ~ but I remind you, this problem was given a child.) 

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alexb
Charter Member
2673 posts 
Sep1802, 05:49 PM (EST) 

4. "RE: drawing puzzle"
In response to message #3

LAST EDITED ON Sep1802 AT 05:50 PM (EST) >I agree, Alex ~ yet sending her on a yearslong futile >search (for a solution for a problem known to >have no solution) could be considered a "waste".
 Is suggesting to search for "Euler path" at my site implies "sending her on a yearslong futile search"? Have you tried?
 The problem has a solution, albeit negative, as you demonstrate below.
>An "even" vertex is one which has an even number of line >segments emanting from it. >The center of the X has 4 segments; it is even. >The peak of a "roof" has 2 segments; it is even. > >Elementary graph theory states: a figure is "traversable" if >(1) all vertices are even, or >(2) there are no more than two odd vertices. Is making a reference any worse than typing the same thing anew? A reference to a general approach gives one a fighting chance to use one's brain. What goal is achieved by giving the solution away? 

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Soroban
Member since Sep1002

Sep1902, 05:01 AM (EST) 

5. "RE: drawing puzzle"
In response to message #4

>Is suggesting to search for "Euler path" at my site >implies "sending her on a yearslong futile search"? Have >you tried? I repeat: Martin was given this problem at about age 8; his daughter may be approximately the same age. I have no objection to suggesting a search for "Euler path", any more than recommending an introductory Topology text. >Is making a reference any worse than typing the same thing >anew? A reference to a general approach gives one a fighting >chance to use one's brain. What goal is achieved by giving >the solution away? I seem to have angered you, Alex  certainly not my intention. I gave the solution to Martin to do as he wishes. If he wants his daughter to use her brain, he can withold the truth. If he truly feels he wasted valuable time in a futile endeavor, he should be given the opportunity to decide for his daughter. But I'll practice more descretion in future positings  promise! 

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fustrated
guest

Aug1806, 02:43 PM (EST) 

9. "RE: drawing puzzle"
In response to message #8

So can any of you morons simply answer "yes" or "no" to the problem and provide a suitable link to a webpage. Or are you just going to carry on quoting each other? 

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kfom
guest

Aug2406, 07:33 PM (EST) 

11. "RE: drawing puzzle"
In response to message #9

>So can any of you morons simply answer "yes" or "no" to the >problem and provide a suitable link to a webpage. Or are you >just going to carry on quoting each other? Well, frustrated, I'll save you the trouble of looking through the _whole_entire_thread_(who knows how long that might take)by quoting select tidbits of info. Soroban wrote: >With more than two odd vertices, the traversing is impossible. >(And the given problem has four odd vertices.) Alex B. wrote: >Search the Web or this site for "Euler path" or "Unicursal Drawings." I write: we're still quoting each other. 

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darya
guest

May0908, 06:53 PM (EST) 

31. "RE: drawing puzzle"
In response to message #9

>So can any of you morons simply answer "yes" or "no" to the >problem and provide a suitable link to a webpage. Or are you >just going to carry on quoting each other? this made me laugh, thanks haha


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krysta
guest

Jan2908, 05:15 PM (EST) 

28. "RE: drawing puzzle"
In response to message #7

and what about half circles on all sides of the box? i know it isnt impossible because ive watched other people figure it out and i have done it but i dont remember..... im not answering your question im just adding on to it. 

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Rod H
guest

Aug2906, 07:33 PM (EST) 

12. "RE: drawing puzzle"
In response to message #3

>Elementary graph theory states: a figure is "traversable" if >(1) all vertices are even, or >(2) there are no more than two odd vertices. > >Consider: When you pass through a point, you have made it an >even vertex ~ one path in, one path out. A vertex is odd if >(1) you start at that vertex, or (2) you end at that vertex. >(It may take some sketching to understand these statements.) Seems clear so far. Like laying out a string, it has no odd vertices if the ends are tied together. >If there is one odd vertex, we must start at that vertex. >And the rest of the figure (all even) can be traversed. Huh? Just curious, how is one odd vertex possible? I can't seem to visualize it. 

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krysta
guest

Jan2908, 06:13 PM (EST) 

29. "RE: drawing puzzle"
In response to message #1

>>My third grade math teacher gave us a drawing puzzle I'm >>still trying to solve thirty odd years later. Now my >>daughter's trying to figure it out and I don't want her >>wasting as many hours on this as I did. > > > >> >>The first excercise is to draw something that looks like a >>house with an "X" in the bottom square without lifting the >>pen or doubledrawing a line. That's easy enough. >> >>The next step is to add the triangular rooflike thing on >>each of the 4 sides of the box with the "X" in it. That I >>can't seem to do (within the rules above). Nor can I figure >>out why it's impossible. > > > >>Is this a popular puzzle? > > > >>Can anyone out there help me >>solve it before my daughter throws away the best years of >>her life trying to solve it? > its actually really simple.. c _ b draw this  point a (start at the bottom) d then make the top "roof" thing /\e then go down diagonally to the bottom left d /\ c_/__\_1b 2e /  /  a f
then go across horizontally to your beginning point (the bottom right corner) you should have this. d /\ c _/__\_ / 1b& 2e /  _/___point 1a 2g f sry if the letters confuse you... ignore them if they do..
the numbers mean which point they are first. kay so then you go up diagonally to the top left corner. d /\ 1c 2h/__\ \/ 1b& 2e /\  _/__\ f point 1a 2g then finish it off by drawing a line downwards ta daaa
d /\ 1c.2h /__\  \/ 1b.2e  /\  /__\ 1f.2i point 1a.2g and sorry to you very smart talking people if i did not use an adequate supply of mind challenging terms that the average person cannot comprehend 

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lb
guest

Sep2806, 04:19 PM (EST) 

13. "RE: drawing puzzle"
In response to message #0

I have solved your puzzle. Line 1 is leading up to the top left corner of the square, part of the X. Line 2 is the begining part of the triangle leading up to the triangles point. Line 3 is coming back down from the point of the triangle. Line 4 is the right side of the square. Line 5 is the bottom of the square. Line 6 is the left side of the square. Line 7is te top of the square and the base of the triangle. Line 8 is the last piece of the X leading to the bottom left corner of the square, finishing the shape.  LB 

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loyalsarah
guest

Mar1507, 10:27 PM (EST) 

14. "RE: drawing puzzle"
In response to message #13

your wrong i have tried to follow your explanation and your wrong it is not posible i have looked it up on many sit's unless you fold over the paper it is imposible in order to do it you woud have to draw an x inside the square first and that is impossible 

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dismal
guest

Apr3007, 06:11 AM (EST) 

15. "RE: drawing puzzle"
In response to message #14

maybe i'm a genius but follow the directions as follows make a line like _ moving from right to left then make the line / moving from bottom to top then make the line  from right to left, this yields the shape z from the top of the z where your pencil should be draw ^ across the top of z where those 2 points intersect draw  from top to bottom (or just simply down) now draw \ through the center of your figure from right to left now draw  from top to bottom now send me money 

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Davaal
guest

May2907, 09:02 AM (EST) 

19. "RE: drawing puzzle"
In response to message #16

Did you ever get an answer to this drawing problem. My friend showed me this one yesterday and told me he knew the answer. He wont give it to me yet and wants me to figure it out. It is possible to do it but all the experts say it can't be done. 

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ethveg
guest

Aug0307, 06:39 AM (EST) 

24. "summarizing"
In response to message #22

It'seems there's a communication gap here. I will quote only the two relevant statements: Elementary graph theory states: a figure is "traversable" if (1) all vertices are even, or (2) there are no more than two odd vertices. So the first puzzle asked about, namely a square with its diagonals and a twoline "roof" on one side (wlog say the top) IS drawable: It has FIVE vertices: the point at the top of the roof has two lines, so it's even. Each upper corner of the square (the corners which "support" the roof) is even: from it emanate one roof line, two sides of the square, and one line of the X, a total of four lines. And each lower corner is odd, being the intersection of two sides of the square and one line of the X. Thus there are exactly two odd vertices, and so by rule (2) above the figure is traversable (drawable, "w/o lifting your pencil or tracing a line.") When we change the figure by adding three more rooves, one on each of the other three sides, each of the FOUR corners of the square is then the intersection of two sides of the square, one side of each of two rooves (making four lines so far) and one line of the X, making a total of FIVE lines; thus each corner, of which there are FOUR, is an odd vertex. Therefore, by rule (2) above, that figure is not traversable and so cannot be drawn in the prescribed manner. And turning the four rooves into a circle (as in the posted figure) doesn't change anything. In graph theory all that matters is whether or not two points are connected by a path: the "shape" of the path is literally meaningless in that theory. The equivalence can be verified by examining in the diagram the intersections at each corner of the square, seeing that they're the same ones I named above for the fourroofed square, and so realizing that only the endpoints matter. 

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abby
guest

Jun1407, 04:29 PM (EST) 

20. "RE: drawing puzzle"
In response to message #0

ok heyy im 12 years old and i solved your puzzle what you do is you draw a backwords L then add another line across to make a triangle then you draw a line up from the triangle makeing a L with a triangle in the center next you draw a trangle top on the top after that you draw a line across under the triangle makeing a house with one line in the center next draw the other line across the center making the X and thats how you make a house with an X in the middle without lifting your pen, pencil, crayon, and soo onn!!! 

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SickSicka
guest

Aug2507, 02:59 PM (EST) 

25. "Answer"
In response to message #0

I heard you could fold the paper. Okay, first off fold the paper. then draw a diagnol line on the normalunfolded part. this will represent half the x. then draw a box on the unfolded part next draw the semicircles, but before you get to the last one, draw the semicircle on the folded piece. you should be stuck. now unfold the paper and do the semi circle again, followed by the other diagnol line. VOILA! Your pen never left the paper, you never drew over a line. 

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Jeny
guest

Sep1010, 06:05 PM (EST) 

33. "RE: drawing puzzle"
In response to message #0

It's easy start out drawing diagonally from bottom to upper right corner. Then move the pen down vertically. Then frm where ur pen is move the pen horizontally to the left. Go vertically up. U should now be on the upper left corner. Move the pen horizontally to the upper right corner. Then slant up to the "tip of the roof". Slant down back to the upper left corner. Draw the last diagonal line back to the bottom right corner. Then u r done!!! :) 

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David W.
guest

Dec0610, 11:32 PM (EST) 

34. "RE: drawing puzzle"
In response to message #0

Start by drawing a line from left to right on the bottom. Now draw a diagonal from the bottom right to the top left. Now draw a line on the top from left to right. Now draw a diagonal line from the top right to the bottom left. Now draw a line from the bottom left to the top left. Now draw a diagonal line from the top left to create the point of the roof. Now draw a diagonal line from there to the right. Then draw a straight line down on the right and you are finished. 

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