1) Find a match using the following tiles: {[100|0], [1|011], [0|01] , [01|010], [10|0], [0|1] }.

A match is [0|01], [10|0].

2) Argue why there is no match for the tiles {[0|00], [11|0], [01|10]}.

There will be not match because you would need to start with either [0|00] or [01|10] for the first and last characters to match. Moving one position up for both causes it to no match immediately.

0|01][100|0][1|011][10|0] The first tile in the sequence has to have the same character on the "top" and "bottom" of its tile. The only tile that fits this description is the tile [0|00], so we have to start with that one. Our next tile has to begin with a zero in its top part, so we can only choose either [0|00] or [01|10]. We can't choose [0|00] since we would end up with [0|00][0|00], giving a 00 on top and 0000 on the bottom and there will be no possible next moves. Thus, the next move must use [01|10], and we have the sequence [0|00][01|10], which is 001 on the top and 0010 on the bottom. Again, because of the extra zero on the bottom, the next moves are limited to [0|00] and [01|10]. We can't pick [0|00] because then we would end up with [0|00][01|10][0|00], which is 0010 on the top and 001000 on the bottom, which has no possible next moves. So, we have no choice but to go with [01|10], which nets us with [0|00][01|10][0|00][01|10], which is 001001 on the top and 00100010 on the bottom. There is no way for the top halves of the tiles to "catch up": this is why there is no match for the tiles {[0|00],[11|0],[01|10]}.

A match could be [100|0][0|1] for there to be a match it has to have the same first character on both the top and bottom and there are none like that so there is no match