-2
$\begingroup$

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? 8x8GRIDwith trominoes

$\endgroup$
2
  • $\begingroup$ 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) $\endgroup$
    – Bubbler
    Dec 2, 2021 at 7:52
  • 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. $\endgroup$ Dec 3, 2021 at 3:42

1 Answer 1

4
$\begingroup$

Yes, there is a solution that involves 2 corner color shares. In this instance, blue and yellow. solution

$\endgroup$
4
  • $\begingroup$ But are rectangular 3x1 or 1x3 trominoes allowed? $\endgroup$ Nov 28, 2021 at 15:00
  • $\begingroup$ I woule have to assume so. The question just asks for trominoes, no specifics on which type. $\endgroup$ Nov 28, 2021 at 17:46
  • 1
    $\begingroup$ All trominoes are as shown in the example.. $\endgroup$ Nov 28, 2021 at 21:59
  • 1
    $\begingroup$ You could have clarified that better. $\endgroup$ Nov 29, 2021 at 11:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.