Final answer:
No, it is impossible to represent the number -3 with exactly 19 tiles since no combination of 19 tiles can sum up to -3. We need more than 19 tiles if we were to use positive and negative tiles to represent the number -3.
Step-by-step explanation:
To represent the number -3 with 19 tiles, one possible approach is to think in terms of positive and negative tiles. We could have a pile of positive tiles and a pile of negative tiles. If we say that each positive tile represents +1 and each negative tile represents -1, then a combination of positive and negative tiles could result in the total value of -3.
For example, let's have 16 positive tiles and 19 negative tiles. If we pair each positive tile with a negative tile, we would be left with no positive tiles and 3 unpaired negative tiles, which would represent the number -3. However, since we need the total number of tiles to be 19, we cannot do this with 19 tiles alone.
Therefore, it is impossible to represent the number -3 with exactly 19 tiles, because no combination of 19 tiles can sum up to -3.
The rules of mathematics in this case are simple arithmetic addition and subtraction, which tell us how to combine positive and negative numbers to achieve a desired total.