The rule to check the divisibility by 13 is:
Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.
Example: 50661-->5066+4=5070-->507+0=507-->50+28=78 and 78 is 6*13, so 50661 is divisible by 13.
111,111 is divisible by 13 (13 x 8547)
the same with 111,111,111,111 is divisible by 13 (13 x 8547008547)
following the same pattern, we know the fisrt twentyfour 1's are divisible by 13 and the last 24 1's also
11,111,111,111,111,111,111,111,1xx,111,111,111,111,111,111,111,111 can be expresssed as:
(111,111,111,111,111,111,111,111 * 10^26) + (xx * 10^24) + (111,111,111,111,111,111,111,111)
Since the first and the last numbers in parenthesis are divisible by 13, we are looking for those numbers "xx" divisble by 13 (different than 1),
the only chances are:
Everyone says that is impossible because opposite corners on a chess board are the same color.
I agree with that I know that it is impossible, but try to explain it in a different way...
What if you paint all the 64 squares or a chess board of the same color, then it makes it possible????
Say for instance you don't use a chess board, only a board 8x8 without colors on it. HOw do you explain it's not possible to fit the dominos?