It is well-known the solution to the problem of connecting nine dots, arranged in three rows of 3 dots, with four straight lines
, without lifting up the pencil from the paper where they are drawn, and without any tricks at all, like folding the paper, etc...
o o o
o o o
o o o
The question is: given the nine dots above, is it possible to connect them with only 3 straight lines
? The restrictions are the same, that is, without lifting up the pencil from the paper where they are drawn, no tricks allowed, and if you retrace a line, you must count one more line.Prove your answer!
Note: this is a revisit to the problem Nine Dots
already posted in this site and you can use that drawing for reference.
When this problem was being analyzed by the "staff", Richard asked me if the dots were "mathematical" dots, or thick as it appears in the drawing (his answer below proves the impossibility for "mathematical" dots).
What I answered to him, IŽll post now : in this problem, and in others similars about connecting dots (12 dots, 16 dots, etc...), wherever they appear (in books of mathematical recreations), nobody can deny that it is never stated that the dots are "mathematical" dots, and in fact, the solutions to them, shows dots with no zero radius.
The "no tricks" clause is to avoid the solution that involves folding the paper, and with only one line youŽll be able to connect them.
Because of this, and by suggestion of the staff, I mentioned the problem of nine dots (with 4 straight lines), and stated tacitly : YOU CAN USE THAT DRAWING FOR REFERENCE. And that drawing has only two dimensions !!!
Posted by pcbouhid
on 2005-07-15 18:05:06