20060203, 05:28  #1 
Nov 2005
2·7·13 Posts 
Dot puzzle
Using only 4 lines, and not picking your pencil up, could you cross all 9 of these dots if this was printed?
Are there methods to go lower? How low can you go? 
20060203, 06:33  #2 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Dot Puzzle
Nibble4bits this has come up before if my memory serves me right so I wont spoil your problem even by spoilerising the answer. What do you mean by going low? you can even go higher depending where you start. Mally Last fiddled with by mfgoode on 20060203 at 06:33 
20060203, 12:49  #3 
Aug 2005
Brazil
2·181 Posts 
I love this solution!

20060203, 12:50  #4 
Aug 2005
Brazil
16A_{16} Posts 
Seriously speaking...

20060203, 15:07  #5  
Bronze Medalist
Jan 2004
Mumbai,India
804_{16} Posts 
Quote:
Mally 

20060203, 20:15  #6 
Aug 2003
Snicker, AL
7·137 Posts 
Fetofs was being facetious.

20060205, 18:03  #7 
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
I think we've discussed this one before
as long as the dots (or the width of the pencil mark) cannot be taken arbitrarily small and the paper we write on CAN be taken arbitrarily large, the solution is 3 lines 
20060207, 15:26  #8 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Dot Puzzle
:surprised Three straight lines TravisT ? I'd like to see your solution.
Please oblige. Mally 
20060207, 18:20  #9  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10100110111010_{2} Posts 
Quote:
If the dots are large enough, of diameter at least as wide as the diagram, a single line suffices, even if it is of zero width. Paul 

20060208, 03:54  #10  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Dot Puzzle
Quote:
Your "IF" s offends my mathematical classical sense.! Lets not bend the rules of the game and stick to the definitions of Euclid which has stood good for over two millenniums. I reiterate Line: has only length and no breadth. Point: that which has position and no dimensions. It would be better if you used a single curved line which is not restricted in the problem instead of using quadrilaterals and circles. Mally 

20060208, 07:42  #11  
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Quote:
thus imagine a rectangle of width r that is just large enough to cover the top row of 3 dots. Draw a line that passes through one corner to the other, since it has nonzero width, the line is not parallel to a line through the centers of the dots and thus will intersect the line that bisects the 2nd row. Create a new line through the bottom row by translating the first line down. Similar to the original line, this will also intersect the middle line, thus we have 3 lines that intersect all 9 dots 

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