A colorful number is one that has no two identical digits. The mirror image of the colorful number 736251 is the number 152637. What is the smallest and the largest four-digit result we can obtain by correctly multiplying two colorful numbers, one of which is the mirror image of the other?

(Bednářrová)
1. Let's first look for the largest four-digit result. From the problem statement, it is clear that we need to multiply the largest possible two-digit numbers. The largest two-digit number is 99, but it is not colorful. The next number is 98, which is a colorful number, and the desired result is

$$
98 \cdot 89=8722
$$

The largest four-digit result is 8722. (2 points)

2. Now let's consider the smallest possible four-digit product. Of course, we will start by looking for the smallest numbers that, when multiplied by their mirror image, give a four-digit number. Let's list the possible candidates: $16 \cdot 61=967$ is not a four-digit number, $17 \cdot 71=1207$ (18, 19 will be larger), $23 \cdot 32=736$ is not a four-digit number, $24 \cdot 42=1008$ (25, 26, ... will be larger), $34 \cdot 43=1462$. The smallest four-digit result is 1008. (4 points)