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1

The answer seems to be


4

I wrote a little program to brute-force this. I can confirm that there appear to be no solutions. If we delete tip 1 there are two; if we delete tip 2 or tip 6 there are still none; if we delete tip 3 or tip 4 there are eight; if we delete tip 5 there are four; if we delete tip 7 there is exactly one solution. So the trouble is unlikely to lie in tip 2 or 6;...


2

Since the 3x3 covers most of the 4x4, we only need to add to it with two lines.


1

Here is my edited answer with the tiny lines removed ]1


2

My answer:


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