# Trails on a grid filled with skinny tetrominoes

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.

• 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?
– Deusovi
May 20 at 1:06
• 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. May 20 at 1:16
• So like creating a maze where we need to pass through all bases? May 20 at 5:25
• I presume this question is the tetromino analogue of this one, is that correct? May 20 at 15:09