Magazine Puzzle Fun

When I add this Brasilian Domino Stamp to my collection I thought of this puzzle.
The objective is to include the most quantity of pieces with this conditions:

1)You add a new piece as in domino, same number with same number

2)Pieces can not touch with others (except of course the one you are joining)

3)The sum of the numbers in each row and column should be always different

For example in the stamp the first piece is 1-3, so the columns are 1 and 3, and the row is 4. The second piece is 3-2 so the columns are 1 and 8, and the rows are 4, 3 and 2. The third piece is 2-5 so the the columns are 1, 8, 2 and 5, and the rows are 4, 3 and 9, we have numbers 1,2,3,4,5,8,9 all differents.

Other example:

The first piece is 3-4, so the columns are 3 and 4, and the row is 7.

The second piece is 4-2, the columns are 3 and 10, and the rows are 7, 4 and 2.

The third piece is 2-2, the columns are 2, 5 and 10, and the rows are 7, 4 and 6.

This is NOT a valid position because pieces 3-2 and 3-4 are in touch.

The fourth piece is 5-3, the columns are 2, 13 and 10, and the rows are 5, 3, 7, 4 and 6.

The fifth piece is 5-1, the columns are 2, 13, 15 and 1, and the rows are 11, 3, 7, 4 and 6.

In this case I think it is not possible to add the sixth piece.

Example: 17 pieces

Piece 1 is 6-5, the columns are 5, 6 and the rows is 11.


Piece 2 is 6-4, the columns are 5, 6, 10 and the rows are 4, 17.


Piece 3 is 4-3, the columns are 5, 9, 14 and the rows are 7, 4, 17 .


Piece 4 is 6-3, the columns are 6, 8, 9, 14 and the rows are 16, 4, 17 .


Piece 5 is 6-6, the columns are 12, 6, 8, 9, 14 and the rows are 22, 10, 17 .


Piece 6 is 6-1, the columns are 19, 6, 8, 9, 14 and the rows are 22, 10, 23, 1.


Piece 7 is 1-1, the columns are 20, 7, 8, 9, 14 and the rows are 22, 10, 23, 1, 2.


Piece 8 is 3-1, the columns are 20, 7, 9, 12, 14 and the rows are 22, 10, 23, 1, 6.


Piece 9 is 5-3, the columns are 20, 7, 9, 12, 17, 5 and the rows are 22, 10, 23, 1, 14.


Piece 10 is 5-1, the columns are 20, 7, 9, 12, 17, 5, 6 and the rows are 22, 10, 23, 2, 19.


Piece 11 is 4-1, the columns are 20, 7, 9, 12, 17, 5, 11 and the rows are 22, 14, 24, 2, 19.


Piece 12 is 4-0, the columns are 20, 7, 9, 12, 17, 5, 11, 4, 0 and the rows are 22, 18, 24, 2, 19.


Piece 13 is 6-0, the columns are 20, 7, 9, 12, 17, 5, 11, 4, 6 and the rows are 22, 18, 24, 8, 19.


Piece 14 is 6-2, the columns are 20, 7, 9, 12, 17, 5, 11, 4, 6, 8 and the rows are 22, 18, 24, 14, 21.


Piece 15 is 2-0, the columns are 20, 7, 9, 12, 17, 5, 11, 4, 6, 10 and the rows are 22, 18, 24, 14, 21, 2.


Piece 16 is 0-0, the columns are 20, 7, 9, 12, 17, 5, 11, 4, 6, 10 and the rows are 22, 18, 24, 14, 21, 2, 0.


Piece 17 is 3-0, the columns are 20, 7, 9, 12, 17, 8, 11, 4, 6, 10 and the rows are 22, 18, 24, 14, 21, 2, 3.

Ariel Futoransky from Argentina made a computer program that found the 155 different 28 pieces solution to this problem with the condition of start with one piece and go only in 1 direction.
The columns sums are: 18, 8, 14, 7, 24, 5, 21, 29, 27, 2, 4, and 9.

The rows sums are: 20, 17, 30, 13, 19, 12, 0, 10, 15, 25, 6 and 1.


The columns sums are: 6, 1, 9, 0, 11, 30, 12, 27, 19, 15, 24 and 14.
The rows sums are: 28, 18, 13, 29, 3, 34, 5, 7, 10 and 21.

You can downlown here the 155 solutions

Ariel Futoransky also found solutions for bigger sets:

Double 8, 45 pieces:
Double 10, 66 pieces:

Then I asked Ariel if it was possible to find a closed circuit, and he found:

Double 6, 28 pieces:








Double 8, 45 pieces:

Double 10, 66 pieces:

Then I asked Ariel Futoransky to find solutions using different numbers:

1)Numbers from 1 to 7






2)Fibonacci Numbers (1,1,2,3,5,8,13)





3)Prime Numbers (2,3,5,7,11,13,17)

Ariel think that this 19 pieces solution is the one that uses the most quantity of pieces in a way that if you add 1 (or N) to each number it is still a solution