Problem 1. Little Know-Not has five cards with digits: $1,2,3,4$ and 5. Help him form two numbers - a three-digit number and a two-digit number - from these cards so that the first number is divisible by the second. $\quad[3$ points] (A.V. Shapovalov)
Answer. $5|3| 2$ and $1 \mid 4(532: 14=38)$ or $2|1| 5$ and $4 \mid 3$ $(215: 43=5)$.

Comment. Of course, this problem is solved by trial and error, but it is useful to use the properties of divisibility of numbers in the process. For example, when selecting a two-digit number, you don't need to consider:

a) neither 15, nor 25, nor 35, nor 45 (it is impossible to form a number divisible by 5 from the remaining cards);

b) neither 24, nor 42 (it is impossible to form an even number from the remaining cards);

c) neither 12, nor 32, nor 52 (it is impossible to form a number divisible by 4 from the remaining cards);

d) 54 (it is impossible to form a number divisible by 9 from the remaining cards).

But even after taking these considerations into account, some trial of options remains, which is faster to handle with a bit of luck and what is usually called "number sense".