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$\begingroup$ The intended solution is the first one with the four lines. The question clearly uses the word "dot", not "disc".
53 1 4. hint: two lines are out the square. – chenbai. Feb 26, 2015 at 12:49. 1. Three horizontal segments and one vertical segment, each passing through three of the points, seem to do the job. I guess it depends on what you mean by "unite them all".
The aim of the Nine Dots Puzzle is to draw a path connecting 9 dots arranged in a $3\times 3$ grid using 4 continuous straight lines, never lifting the pen/pencil from the piece of paper. A solution is displayed below (spoiler alert):
This means that the the above puzzle requires 5 lines. The angle of each of the lines must be a multiple of 45. If needed, a point can be connected by multiple lines. Right now, my best method is to create a spiral of lines, which uses 2N − 1 2 N − 1 lines. However, I can't prove that this is the minimum number of lines needed.
It is impossible to connect all the dots using only three lines, which gives us the minimal number of lines for n = 3 n = 3 with k3 = 4 k 3 = 4. For n = 2 n = 2, we easily see that k2 = 3 k 2 = 3: For n ≥ 4 n ≥ 4 we can use the trick we used for n = 3 n = 3 and then just expand from there: This gives us k4 ≤ 6 k 4 ≤ 6 (using what I ...
$\begingroup$ @NKLost You'll also have to be more clear about how you are connecting the dots. In my mind, connecting 3 dots yields three lines, and 4 dots yield 6 lines. I also see ways in which 234987 dots yield one line. $\endgroup$ –
It's well known that it requires an unbroken path of $4$ straight lines to cover all $9$ dots in a $3$ by $3$ lattice grid (see here). By making use of the $4$ -line path in $3\times 3$ grid, it only needs $14$ lines to cover the three-dimensional $3\times 3\times 3$ grid ( $4$ lines for each layer and $2$ lines for layer connection, which ...
Only straight lines can be used to connect the dots. At least 4 dots must be connected. If you connect 2 dots directly, when there's a dot in between, it will also be crossed (so if you try to connect 1->3, you'll actually connect 1->2->3). This rules exist if rule #6 is not in effect. Diagonal lines are allowed (you can connect from 2->6, even ...
If we do the order $5$ triangle we have $15$ dots, three lines with five dots, three with four dots, and six with three dots. The new ones with three dots run from a corner through the center to the middle of the other side. This gives $\frac 12\cdot 15\cdot 14-3\cdot 9-3\cdot 5 -6\cdot 2=51$ lines
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