Let's have an 8x8 GRID to be filled with L-trominoes of 3 different colors. 64 squares leave room for 21 trominoes, so there should be 7 trominoes of each color and one empty square. Trominoes of the same color are not allowed to touch side-to-side anywhere.
In the presented example, there is an empty square in the position B3; trominoes of the same color touch corner-to-corner in two places marked with red. With the empty square in the B2 position (that is, one row higher), can you fill the grid with L-trominoes, such that trominoes of the same color touch corner-to-corner in only 2 places? 
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asked Nov 27, 2021 at 21:27
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$\begingroup$ Does this satisfy "trominoes of the same color touch corner-to-corner in only 2 places"? Corner-to-corner touch occurs three times but at two places. (This is not an answer because it has 8 grays and 6 blues) $\endgroup$– BubblerDec 2, 2021 at 7:52
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1$\begingroup$ The question is specific...only two places is it allowed for trominoes to touch corner-to-corner. In your example you have thee places where trominoes meet corner-to-corner and the number of each color tromino is not equal. $\endgroup$– Vassilis ParassidisDec 3, 2021 at 3:42
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1 Answer
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Yes, there is a solution that involves 2 corner color shares. In this instance, blue and yellow.
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$\begingroup$ But are rectangular 3x1 or 1x3 trominoes allowed? $\endgroup$ Nov 28, 2021 at 15:00
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$\begingroup$ I woule have to assume so. The question just asks for trominoes, no specifics on which type. $\endgroup$ Nov 28, 2021 at 17:46
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1$\begingroup$ All trominoes are as shown in the example.. $\endgroup$ Nov 28, 2021 at 21:59
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1$\begingroup$ You could have clarified that better. $\endgroup$ Nov 29, 2021 at 11:52