3. Find the smallest number that gives a remainder of 1 when divided by 2, and a remainder of 2 when divided by 3.
3. First, let's write down the numbers that give a remainder of 1 when divided by 2:

$$
3,5,7,9,11 \ldots
$$

Next, let's write down the numbers that give a remainder of 2 when divided by 3:

$$
5,8,11,14,17 \ldots
$$

We will choose from the obtained numbers the one that satisfies both conditions and is the smallest. This number is 5.

We could have reasoned differently. After writing down the numbers that give a remainder of 1 when divided by 2, we find which of them will give a remainder of 2 when divided by 3, and then choose the smallest one among them (5, 11, 17 ...), or we could first write down the numbers that give a remainder of 2 when divided by 3, and then choose the smallest one among them that gives a remainder of 1 when divided by 2.

Answer: 5.