7.4. In a table containing $A$ columns and 100 rows, natural numbers from 1 to $100 \cdot A$ were written in ascending order, starting from the first row. The number 31 is in the fifth row. In which row is the number 100?
Answer: in the 15th row.

Solution. From the condition, it follows that $A \leq 7$, since for $A \geq 8$ the number 31 would be located before the fifth row. Similarly, we get that $A \geq 7$, otherwise the number 31 would be located after the fifth row. Therefore, $A=7$. Since $100=7 \cdot 14+2$, the number 100 is located in the 15th row.