Can You Solve It?

Hello there.. 

I'd like to share with you one of the problems which I read once in A problem solving book.. I wonder if anyone knew it, and subsequently could answer it.. 

Now, see the circles on the right side. It is required to cross these circles with max. 4 straight lines, but the lines must be connected. It means you can't raise your hand off the paper when you want to make the next line.. 

PS: this problem has more than one solution. Now, let's see about yours.. 

Please note that comments will be moderated in order to allow more numbers of people participate in it. That means if anyone gives the correct answer, it will not be revealed to others in the early beginning :)

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  • Unfortunately, I can't send the drawing now, but I can say that the solving is possible only with nine circles but not with dots. It was my mistake when I tried to connect the circles as if they were dots. Thanks for the challenge and for the hints. The drawing may be later.

  • Congratulations valentina :D

    Finally, it seems we have an answer.. please do a schematic drawing and share it here with us here.. I will end moderating comments in order to make it easier for you.. The problem, as I said, has more than one solution.. So, please share it and let others find their ways to discovering more solutions :D

    Thank you so much for tiring your brain in this problem, valentina.. please follow the next blog where I will tell a real story from life where similar problem appeared and how brilliantly it was solved :D

    Thanks again :) 

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  • Hi dear AG,

    Your hints are really very useful.Using them I've managed to solve the problem. My four lines look like a long (or tall) letter M or similar to it. But I'm quite upset realizing how stupid I really am because my thinking is so limited. Before reading your hints my way of thinking was imprisoned in a small square. It's sad.

  • Well guys, one more but last hint I can give.. After this hint, if nobody is about to solve it, I will give one of the solutions.. for now, let me tell you the hint:

    You guys, don't have to cross the circles in the center... nobody tells that the line that you will draw must cross the center.. it's your brains who tell that.. even if you are able to cross the circles from periphery, it will be correct..

    No, I wish somebody can catch it.. 

  • I think I am not clever enough :(. I've never seen before. Hope I know the answer soon..:)

  • or let me say, try to draw the circles in a small place in the middle of the paper.. you did so? OK, now think about the wide space of the paper (not about the narrow space of the shape) and try to use this wide space better :) 

  • Luci, in more words.. the shape deceives you to think about columns and rows.. don't allow the shape to show you that you have to cross the circles in a regular way.. and if you keep thinking the same way, you will never find a solution for this problem.. that's why you need to get out of the shape illusions, and think wider.. if you could do that, you will find many solutions, and you will feel it is very easy :) 

    This will be my second hint. Don't think about rows and columns. Get out of the shape illusions.

  • If i just do four lines around this square and make the circles hidden there..guess it is wrong as they arent connected..just trapped :D
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