You can't make a loop, without using one of the dots twice.
. That is true but you can loop in your line as long you do not go over your line
* * * *
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You can start at the red dot, make the loop, and then end at the blue dot.
what you say is true but the rules allow you to loop within lines as long as you do not go over them
Think of 100 circles of radii 1, 2, 3, ..., 100 centered at x = 1, 2, 3, ..., 100.
They are mutually tangent at the origin.
Any number - a countable infinity of them - could be mutually tangent.
And none of them "go over" any of the others.
Between circles 1 and 100 there are 98 circles that do not violate the OP.
You would have to add a statement that once two curves are made to touch,
a third such line is prohibited, in order to limit the curves that touch to only two.
So, mentally I will add that statement, and completely agree.