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May 6 In-Class Exercise .

Please post your solution to the May 6 In-Class Exercise to this thread.

Best, Chris

Please post your solution to the May 6 In-Class Exercise to this thread. Best, Chris

-- May 6 In-Class Exercise

Group: Michael, Holly, Gricelda, Jinyin Chai, Keven, Max, Prajesh, Lichun Gao [01|010][0|1][10|0] -> 01010|01010 The set of tiles can not have any matches because:

the first tile must be [0|00] because it is the only tile that matches the first number top and bottom

the top sequence is now shorter than the second sequence so at some point [11|0] must be used

the bottom sequence can never have two consecutive 1's in a row because the only tile with a one on bottom always has a 0 next to it

Therefore to be balanced the top must have 2 consecutive 1's but the bottom can never arrange tiles such that 2 consecutive 1's appear next to each other.

(Edited: 2020-05-06)

Group: Michael, Holly, Gricelda, Jinyin Chai, Keven, Max, Prajesh, Lichun Gao [01|010][0|1][10|0] -> 01010|01010 The set of tiles can not have any matches because: 1) the first tile must be [0|00] because it is the only tile that matches the first number top and bottom 2) the top sequence is now shorter than the second sequence so at some point [11|0] must be used 3) the bottom sequence can never have two consecutive 1's in a row because the only tile with a one on bottom always has a 0 next to it Therefore to be balanced the top must have 2 consecutive 1's but the bottom can never arrange tiles such that 2 consecutive 1's appear next to each other.

-- May 6 In-Class Exercise

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

a possible match is [0|01][10|0]

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

if you start with [0|00] which is the only possible start, you can only continue with [01|10], but that requires you to use [0|00] again, and you will never be able to complete the top row with enough zeroes to match the bottom row.

(Edited: 2020-05-06)

Find a match using the following tiles: {[100|0], [1|011], [0|01] , [01|010], [10|0], [0|1] }. a possible match is [0|01][10|0] Argue why there is no match for the tiles {[0|00], [11|0], [01|10]}. if you start with [0|00] which is the only possible start, you can only continue with [01|10], but that requires you to use [0|00] again, and you will never be able to complete the top row with enough zeroes to match the bottom row.

-- May 6 In-Class Exercise

sebrianne ferguson and ben foley: [100|0][0|01] would be a match

we dont think theres a match because the s's don't have any 1's.

sebrianne ferguson and ben foley: [100|0][0|01] would be a match we dont think theres a match because the s's don't have any 1's.

-- May 6 In-Class Exercise

[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 if we do, we end up with [0|00][0|00], giving a 00 on top and 0000 on the bottom, which has no possible next movies.
Thus, our 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 our 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.
Hopefully, it is becoming clear that the bottom halves of the available tiles only net us excess zeros, and 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]}.

* [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 if we do, we end up with [0|00][0|00], giving a 00 on top and 0000 on the bottom, which has no possible next movies. * Thus, our 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 our 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. * Hopefully, it is becoming clear that the bottom halves of the available tiles only net us excess zeros, and 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]}.

-- May 6 In-Class Exercise

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

Starting tile must have [0|00] since that is the only part that matches for both bottom and top.

Find a match using the following tiles: {[100|0], [1|011], [0|01] , [01|010], [10|0], [0|1] }. ->0|01][100|0][1|011][10|0] is a match. Starting tile must have [0|00] since that is the only part that matches for both bottom and top.

-- May 6 In-Class Exercise

Group: Nick Fulton, Dillon Larson, Osama Hanhan.

A match could be [100|0][0|01] because the first half of the first tile matches with the second half of the second tile, and the second half of the first tile matches with the first half of the second tile. There is no match for the secondary set of tiles because there is no match for the second half of the first tile, the first half of the second tile, or either half of the third.

Group: Nick Fulton, Dillon Larson, Osama Hanhan. A match could be [100|0][0|01] because the first half of the first tile matches with the second half of the second tile, and the second half of the first tile matches with the first half of the second tile. There is no match for the secondary set of tiles because there is no match for the second half of the first tile, the first half of the second tile, or either half of the third.

-- May 6 In-Class Exercise

Group: Sumaiyya, Joshua, Edgar, Gurseerat, Jiajian, Jieni, Tyler

Match: {[0|01], [10|0]} -> 010|010

In order for there to be a match, the first tile must have the same first character on its top and bottom, and the last tile must have the same last character on its top and bottom. There is only one tile that fits this criteria, [0|00]. Since its top does not equal its bottom, it in itself cannot be a match and there are no other possibilities for a match.

(Edited: 2020-05-06)

Group: Sumaiyya, Joshua, Edgar, Gurseerat, Jiajian, Jieni, Tyler Match: {[0|01], [10|0]} -> 010|010 In order for there to be a match, the first tile must have the same first character on its top and bottom, and the last tile must have the same last character on its top and bottom. There is only one tile that fits this criteria, [0|00]. Since its top does not equal its bottom, it in itself cannot be a match and there are no other possibilities for a match.

-- May 6 In-Class Exercise

A match could be [0|01][100|0][1|011][10|0] there is no match for the tiles {[0|00], [11|0], [01|10]} because there is no match for the second half of the first tile, the first half of the second tile, and both half of the third.

-- May 6 In-Class Exercise

There will be no match.

The reason for this is because the top and bottom on the first/last character does not match and there is not enough zero’s to actually complete the round because you will then have to use the same zeros that you already used before.

There will be no match. The reason for this is because the top and bottom on the first/last character does not match and there is not enough zero’s to actually complete the round because you will then have to use the same zeros that you already used before.