Here is a little enigma. You have one sheet of paper (white) and a pen. You need to draw a circle (non-zero radius of course) and its center (just a point) without lifting the pen. How do you do this?

turn it upside down, then lift it over your head and draw the circle and the point. since you're drawing upside-down, you never lift the pen

Haha original solution. That's not the one I expected though. I meant that the pen should stay on the paper all the time.

say u have a square list of paper. you fold a paper at 1/4 and 3/4 of its side so that edges of the fold are touching each other in the middle. Put pen into the center point of the rectangle and then draw a circle on folds and the other side without taking the pen off. Unfold the paper. The center will be marked on one side, the circle on the other, but conditions of the problem are satisfied.

That was the idea. Actually you can even draw the circle on the same side as its center without too much trouble now that you've had the idea to fold the paper (of course there should be no line on between the circle and its center but you're free to draw whatever you want on the back.

QuoteOriginally posted by: JungixHere is a little enigma. You have one sheet of paper (white) and a pen. You need to draw a circle (non-zero radius of course) and its center (just a point) without lifting the pen. How do you do this?There may be another solution without folding the paper. I know that not everyone will agree with this solution.I push the pen perpendicularly to the paper and make a mark as the centre. Then I tilt the pen slowly toward to the surface of the paper such that the pen is parallel to the paper. Te tip of the pen is no longer touching the paper. During the process, the pen is always touching the paper (or at least one atom of the pen is touching the paper.) I move the pen away from the dot which I have marked. Again the pen is still touching the paper during the process. As the tip of the pen is not touching the paper, I will not make any line on the paper as I move the pen. Once the pen reaches the location with a distance of radius from the mark, I tilt the pen upward with the pen always touching the paper. Now the tip of the pen is touching the paper and then I draw the circle.

QuoteI push the pen perpendicularly to the paper and make a mark as the centre. Then I tilt the pen slowly toward to the surface of the paper such that the pen is parallel to the paper. Te tip of the pen is no longer touching the paper. During the process, the pen is always touching the paper (or at least one atom of the pen is touching the paper.) I move the pen away from the dot which I have marked. Again the pen is still touching the paper during the process. As the tip of the pen is not touching the paper, I will not make any line on the paper as I move the pen. Once the pen reaches the location with a distance of radius from the mark, I tilt the pen upward with the pen always touching the paper. Now the tip of the pen is touching the paper and then I draw the circle.I think msccubes is a brilliant solution. He solved all problems of this class without caring of any particulars. Now any set of disconnected figures could be drawn with this method without taking a pen from the paper. How about further enhancements. Like using a retractable pen. You mark a center and retract the drawing tip leaving just one atom sticking out. You are still touching the paper with the atom but it doesn't draw anything -- an atom cannot obviously draw, etc. Or even a better idea. Call yourself a pencil. Paint your behind. Sit in a center of the circle. Then turn on your head (you are obviously touching the ground all the time at least with one atom of your body) and then slide to the point of circumference and then turn again and sit on your behind again. Draw a circle. Possibilities are mindboggling with this approach...

I post this idea just wishing everyone has some fun!Have a nice day!