Problem 4. Blagoya participated in a lottery where each ticket is marked with a three-digit number. He bought all the tickets marked with numbers where the product of the tens and units digits is equal to 12, and the sum of these two digits differs from the hundreds digit by 1. How many tickets and with which numbers did Blagoya buy?
Solution. Let $D$ denote the tens digit and $E$ the units digit. According to the problem, the product of the tens digit and the units digit is 12, so the possible pairs $(D, E)$ are: $(6,2),(2,6),(3,4),(4,3)$.

The sum $D+E$ of the first two pairs is 8, so in this case, the hundreds digit can be 7 or 9. Therefore, Blagoya bought the lottery tickets with the numbers 726, 762, 926, and 962.

The sum $D+E$ of the last two pairs is 7, so in this case, the hundreds digit can be 6 or 8. Therefore, Blagoya bought the lottery tickets with the numbers 634, 643, 834, and 843.

Since he bought all the lottery tickets marked with numbers with the given properties, Blagoya bought a total of 8 lottery tickets.