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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".
$\begingroup$ @bof I believe OP meant a polygonal chain of 4 segments containing all the given dots. $\endgroup$ – Andrei Rykhalski Commented Feb 26, 2015 at 12:52
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):
Lines must make a path (the endpoints of each of the lines must connect, except for the first and last line). Lines cannot go out of square. 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 ...
The following is a popular riddle: Draw a $3 \\times 3$ grid, and connect all the dots using only $4$ straight consecutive lines. The solution is to think outside of the box and do the followin...
$\begingroup$ @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. $\endgroup$ –
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 ...
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 ...
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
Assuming you have a set of nodes, how do you determine how many connections are needed to connect every node to every other node in the set? Example input and output: In Out <=1 0 2 1 3 3 4 6 5 10 6 15