2. How many integers $x, -1000 < x < 1000$ are divisible by 3, and how many integers $y, -444 < y < 444$ are not divisible by 4? Which is greater?
Solution. From 1 to 999, we have 333 numbers divisible by 3, from -1 to -999, we have another 333. Zero is also divisible by 3, so we have $333+333+1=667$ possibilities.

For numbers from 1 to 443, we have $443=4 \cdot 110+3$, meaning there are 110 numbers divisible by 4, from -1 to -443, there are another 110, plus zero, giving us $110+110+1=221$ numbers divisible by 4 from -444 to 444. From -444 to 444, there are 887 numbers, so we have $887-221=666$ numbers not divisible by 4. Therefore, there are more numbers from -1000 to 1000 that are divisible by 3.