Each letter in the table represents a certain natural number (the same letters represent the same numbers). We know the sums of the values in the third row, in the fourth row, and in the first column. Determine at least one suitable quadruple of numbers that can replace the letters $A, B, C, D$.

| $D$ | $A$ | $C$ | $B$ |  |
| :---: | :---: | :---: | :---: | :---: |
| $C$ | $B$ | $D$ | $A$ |  |
| $B$ | $C$ | $B$ | $C$ | 50 |
| $D$ | $A$ | $A$ | $A$ | 45 |
| 85 |  |  |  |  |

( $\check{S}$. Ptáčková)
In the third row, the sum $B+C$ appears twice and the total sum is 50. Therefore, $B+C=25$.

In the first column, the sum is $B+C$ plus $2D$, and the total sum is 85. Since $B+C$ is 25, $2D=85-25=60$. Hence, $D=30$.

In the last row, $D+3A$ appears, and the total sum is 45. Thus, $3A=45-30=15$, so $A=5$.

We choose the quadruple of numbers $A, B, C, D$ such that $A=5, B+C=25, D=30$.

For example, the quadruple $A=5, B=10, C=15, D=30$ works.

(The problem can also be solved using equations that describe the above reasoning.)

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