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Let's have a 10x10 grid with 12 empty bases. The rest of the grid is filled with skinny tetrominoes. The 5 regular tetrominoes are marked with a red color and the 2 reflections are marked with a green color. Each base is marked with an orange color.

The following conditions apply:

  1. The trail has to be continuous.
  2. The trail is allowed to make only one angle on each square.
  3. The trail is allowed to pass only once through each square.
  4. The trail is not allowed to cut any tetromino.
  5. It is mandatory that each of the the 7 tetrominoes appears a minimum of 3 times.
  6. The trail must pass through all the bases.

With the above conditions what is the maximum number of squares through which a trail can pass? You can put the bases anywhere you please on the grid.

may19

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    $\begingroup$ I don't quite get what's going on here - tetrominoes are shapes made up of shaded cells. Here it seems like you have some rule for converting those to lines, but it's not completely clear how you're doing that - what exactly counts as "cutting" a tetromino? $\endgroup$
    – Deusovi ♦
    Commented May 20, 2021 at 1:06
  • $\begingroup$ What I mean by cutting is is that the trail cuts through the red and green lines of the skinny tetrominoes . As you can see, the trail shown above does not cut any skinny tetromino. $\endgroup$
    – Vassilis Parassidis
    Commented May 20, 2021 at 1:16
  • $\begingroup$ So like creating a maze where we need to pass through all bases? $\endgroup$
    – justhalf
    Commented May 20, 2021 at 5:25
  • $\begingroup$ I presume this question is the tetromino analogue of this one, is that correct? $\endgroup$
    – AxiomaticSystem
    Commented May 20, 2021 at 15:09

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The O tetromino appears four times, all others appear three times.
Sadly, there's no symmetry to exploit like there was in my answer to the trimino version of this question.
The grid:

enter image description here

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