# 4 walls of domino tower

How can I rearrange the domino tiles below so that all vertical columns has 0,1,2,3,4,5,6. While all the horizontal rows has 0,1,2,3,4,5,6 + duplicate ?

• I'm not sure, what do you mean with "+duplicate"? Could you clarify the question? Commented Oct 19, 2016 at 19:42
• Disclaimer: I don't know how
– TSLF
Commented Oct 19, 2016 at 19:44
• @TSLF if this isn't your puzzle you need to credit the source otherwise it is plagiarism Commented Oct 19, 2016 at 19:44
• I managed to do all vertical but I am not sure if this is possible.
– TSLF
Commented Oct 19, 2016 at 19:59
• By duplicate do you mean you can have one duplicate value. For example row 1 will contain (0,1), (2,3), (4,5),(6,4) where 4 is a duplicate or (0,1), (2,3), (4,5),(6,6) where 6 is a tile with the same value on both sides. And are you supposed to have 2 (5,6) tiles or should the last one be (6,6) Commented Oct 19, 2016 at 20:15

As noted in the comments to the question, the tiles in the picture form a standard set except for an extra 5/6 and a missing 6/6. If we assume the picture to be correct,

It's impossible, as there aren't enough sixes to cover all 8 columns.

Otherwise, making the assumption that we are supposed to arrange a standard set:

Any double already creates a duplicate, so we have to have one double in each row. Therefore, I started by placing all doubles in the first column. To keep the pattern going, I arranged all tiles with a difference of 1 or 6 in the second column, differences of 2 or 5 went in the third column, and finally 3 or 4 in the fourth column:

 00  23  46  51
11  34  50  62
22  45  61  03
33  56  02  14
44  60  13  25
55  01  24  36
66  12  35  40

• Its corrected , (5,6) now (6,6)
– TSLF
Commented Oct 20, 2016 at 17:02