[wolfgang]

If you have a piece of ruler( without graduations)which is 26 cm long.

How can you draw a 29 cm long striaght line on a white paper using this ruler only?

you are not allowed to break the ruler or cut any piece of the paper, the paper is irregular in shape but lagre enough.

(near to 29 is acceptable)...i.e. the difference should be < 0.1

[superprismatic]

May we assume that the short edge is perpendicular to the long 29-cm edge?

[Guest]

Hi, I am sorry to inform you that you cannot draw a line on a sheet of paper using only a ruler, be it a 26 cm or a 29 cm line. I believe you will need a pen do proceed. This may be obvious, but I wanted to point it out because it bothered me to see such nonsense on such a logical website. Please don't be offended by this remark, and anyway it doesn't change the fact that this is a good riddle and I haven't yet figured it out.

[Guest]

I'm dead sure you'll need more than just an X lengthed ruler... for starters a pen or pencil will do... UNLESS the paper is pressure senitive, in which case you could make a mark with the ruler, but then it would be a trouble to make a straight line

[Guest]

Hi, I am sorry to inform you that you cannot draw a line on a sheet of paper using only a ruler, be it a 26 cm or a 29 cm line. I believe you will need a pen do proceed. This may be obvious, but I wanted to point it out because it bothered me to see such nonsense on such a logical website. Please don't be offended by this remark, and anyway it doesn't change the fact that this is a good riddle and I haven't yet figured it out.

I'm dead sure you'll need more than just an X lengthed ruler... for starters a pen or pencil will do... UNLESS the paper is pressure senitive, in which case you could make a mark with the ruler, but then it would be a trouble to make a straight line

I'm sorry, but technically you are both correct and incorrect. If the paper were to be pressure sensitive, then the ruler could be tilted onto its edge, pressed down and either slid or moved to a position that would complete the 29cm line. Also, once the original 26cm line was created, it is fairly trivial to line the ruler back up on the line such that the remaining 3cm can be 'drawn.'

That being said, I haven't yet taken the time to try and solve the riddle myself.

[Guest]

First, draw a 26 cm line. Then try to aim for a 13 cm line, which will be up to half the ruler... Start drawing the second line at the ending point to the first line and parallel to it. These steps will result in having an L shaped figure. Now, just make a third line connecting the starting point of the first line, with the ending point of the second line.

If you perfectly hit the 13 cm mark on the ruler, the resulting third line will be 29.0689 cm long.

[Guest]

I'm sorry, but technically you are both correct and incorrect. If the paper were to be pressure sensitive, then the ruler could be tilted onto its edge, pressed down and either slid or moved to a position that would complete the 29cm line. Also, once the original 26cm line was created, it is fairly trivial to line the ruler back up on the line such that the remaining 3cm can be 'drawn.'

That being said, I haven't yet taken the time to try and solve the riddle myself.

For some reason I can't get the editor to save my changes, so here's what I wanted to add:

Also, the 'line' was not described as being formed in any special way. I can imagine forming a crease in the paper that is near enough to 29cm with defined ends to the crease; this could be described as a line on the paper (I believe there is even an artist that was uses deformations of paper as a medium).

[Guest]

First, draw a 26 cm line. Then try to aim for a 13 cm line, which will be up to half the ruler... Start drawing the second line at the ending point to the first line and parallel to it. These steps will result in having an L shaped figure. Now, just make a third line connecting the starting point of the first line, with the ending point of the second line.

If you perfectly hit the 13 cm mark on the ruler, the resulting third line will be 29.0689 cm long.

[12.6178, 13.0694]

[Guest]

First, draw a 26 cm line. Then try to aim for a 13 cm line, which will be up to half the ruler... Start drawing the second line at the ending point to the first line and parallel to it. These steps will result in having an L shaped figure. Now, just make a third line connecting the starting point of the first line, with the ending point of the second line.

If you perfectly hit the 13 cm mark on the ruler, the resulting third line will be 29.0689 cm long.

I like your answer!

once the 26cm line is drawn, visually divide it in half and make a small mark. Then, place the end of the ruler at this mark and mark on the ruler where the line ends. Place the ruler back against the original line so they line up and compare the marks on the line and on the ruler. If they don't match, visually divide the difference and make a new mark on the line and either erase the previous marks or change them so you know not to use them. Use the new mark to perform the above steps until the ruler and line marks match or are extremely close; you now have a very accurate 13cm and 26cm ruler.

[Guest]

i think that it is logical that pen is to b taken as given in dis situation. even if not , one can use ones nail or rulers edge to draw a line.

well the riddle is easy :

mark the initial point and then use the 26cm ruler thrice to make a point at a distance of 78 cm. then get hte middle point of these 2 lines by folding the paper . from either points the middle point is 29 cm long . now we can draw it with a pen or nail.

[Guest]

sorry the above solution is wrong . i just made a wrong mental picture of 29 being 39...... i m really sorry.......

[Guest]

Draw a line 21 cm long

Draw a line 20 cm long at one end perpendicular to that line

Draw a line from the other end of the 21 cm line to the 20 cm line

This line will be 29 cm long

20^2 + 21^2 = 29^2

400+441=841

[Guest]

That would only work if the ruler had graduations...

Edited July 28, 2011 by mark31121

[Guest]

You draw a line the 26 cm of the ruler.

Then fold the paper using the line as a guide (this way you can find the half way point accurately and create a perpendicular line [not parallel as previously mentioned, an easy mix-up of words..])

At the mid-way point draw another 26 cm line up the fold - Joining up the end points will give a triangle with a hypotenuse of 29.07 cm. You might need a longer straight edge to actually draw the line though...

Other posts are pretty much there, but surely this would be the easierst way.

Edited July 28, 2011 by mark31121

[Guest]

You draw a line the 26 cm of the ruler.

Then fold the paper using the line as a guide (this way you can find the half way point accurately and create a perpendicular line [not parallel as previously mentioned, an easy mix-up of words..])

At the mid-way point draw another 26 cm line up the fold - Joining up the end points will give a triangle with a hypotenuse of 29.07 cm. You might need a longer straight edge to actually draw the line though...

Other posts are pretty much there, but surely this would be the easierst way.

I took it for granted that he meant perpendicular as I saw he was using the Pythagorean equation. To draw the straight line, you could easily line up th ruler's edge with the two end points by viewing the paper at a near 90 degree angle of incidence. To ensure a perpendicular set of lines, you could perform my algorithm for finding the center with both sides of the ruler (of course it just occurred to me that this requires perpendicular ends on the ruler or equivalent-opposite angles to ensure the centers of both sides line up normal to the edge). Then use those markings to line up the ruler perpendicular to the first line, make a small line and use it to draw the next full line.

[Guest]

If it doesn't have graduations, it's not a ruler, only a straightedge.

[Guest]

Draw - 26 cm circles with the center in the perimeters of each other

Draw 2 - 26 cm circles from the intersections of the original 2 circles

This gives enough points for the ruler to be long enough to dissect the 26 cm from the original 2 points lines.

Now that you have the center point you have determined a 13 cm line

Draw a line perpendicular to this 26 cm

Draw a line from the end of this back to the center of the original circle

This line should be 29.068 cm

[Guest]

If the adjacent side of the ruler is at right angle.

Draw a straight line and mark a length say 'x'

as follwoing

|\

y | \ h

| \

-----

x

y = 26

x = some value

apply hypotenuse theorem h = root of(y2 + x2)

substitue h = 29, and get value of x.

hope this would be correct.

[Guest]

26 cm straight and should take help of adjacent side of the scale is drawn straight to the 26cm straight line (by not lifting up)

[Guest]

JAGDMC is dead on. He's exactly correct, the only thing is he didn't quite exactly explain the trick to it, though I'm positive he knew exactly what he was doing, just didn't explain the whole thing to us. He brilliantly used the Pythagorean Theorem, A^2+B^2=C^2, and made a right triangle on the paper! Genius! If you make a right triangle, having the 2 legs drawn to the lengths of 13 and 26cm each respectively, the hypotenuse is exactly 29.06888... which is within the set tolerance for the answer! Thereby, drawing a line connecting the 2 points of the L shape and making this line you've drawn the hypotenuse of a right triangle, it will essentially be 29cm. I hope that clears his answer up a little, that is how he arrived at his solution, and it was quite ingenious to think of it that way. Nice job, JAGDMC!

[Guest]

i think that it is logical that pen is to b taken as given in dis situation. even if not , one can use ones nail or rulers edge to draw a line.

well the riddle is easy :

mark the initial point and then use the 26cm ruler thrice to make a point at a distance of 78 cm. then get hte middle point of these 2 lines by folding the paper . from either points the middle point is 29 cm long . now we can draw it with a pen or nail.

well its going to be 39cm not 29 think again

[Guest]

Draw line of 26 cm than divide the line into two equal part by folding the paper we ill get 13 cm than again fold the paper we ill get 6.5 ans by folding it again we can get 3.25 cm (total three fold is required to get 3.25 cm ) so so draw a line of 3.25 cm and than open the folds and join the 3.25 cm line with the 26 cm line which can be drawn easily with help of ruler and we ill get line of 19.25 cm which is approx 19 cm .

[Guest]

i think that it is logical that pen is to b taken as given in dis situation. even if not , one can use ones nail or rulers edge to draw a line.

well the riddle is easy :

mark the initial point and then use the 26cm ruler thrice to make a point at a distance of 78 cm. then get hte middle point of these 2 lines by folding the paper . from either points the middle point is 29 cm long . now we can draw it with a pen or nail.

78/2 = 39

[wolfgang]

First, draw a 26 cm line. Then try to aim for a 13 cm line, which will be up to half the ruler... Start drawing the second line at the ending point to the first line and parallel to it. These steps will result in having an L shaped figure. Now, just make a third line connecting the starting point of the first line, with the ending point of the second line.

If you perfectly hit the 13 cm mark on the ruler, the resulting third line will be 29.0689 cm long.

Very good...!!

[wolfgang]

You draw a line the 26 cm of the ruler.

Then fold the paper using the line as a guide (this way you can find the half way point accurately and create a perpendicular line [not parallel as previously mentioned, an easy mix-up of words..])

At the mid-way point draw another 26 cm line up the fold - Joining up the end points will give a triangle with a hypotenuse of 29.07 cm. You might need a longer straight edge to actually draw the line though...

Other posts are pretty much there, but surely this would be the easierst way.

Very good!!

[wolfgang]

Thank you all...hope you enjoyed it..