The total was $1+2+\ldots+9=45(\mathrm{dl})$. Each of the three gardeners received the same amount of rods, i.e., $15 \mathrm{dl}(45: 3=15)$, and had it in three glasses $(9: 3=3)$. For each gardener, we need to express the number 15 as the sum of three natural numbers less than or equal to 9. No two of the numbers 9, 8, and 7 can be in the same triplet, as the sum of the numbers in this triplet would be too large. Therefore, each triplet must contain exactly one of these numbers. We ask, in which triplets does 9 appear, in which 8, and in which 7:

$$\begin{array}{lll} 9+5+1 & 9+4+2 & \\ 8+6+1 & 8+5+2 & 8+4+3 \\ & 7+6+2 & 7+5+3 \end{array}$$

The rods can now be divided among the gardeners in only two ways:

- if one gets $9+5+1(\mathrm{dl})$, the second must get $8+4+3(\mathrm{dl})$ and the third $7+6+2(\mathrm{dl})$,
- if one gets $9+4+2(\mathrm{dl})$, the second must get $8+6+1(\mathrm{dl})$ and the third $7+5+3(\mathrm{dl})$.

Note. Students can find suitable triplets by unstructured experimentation, or they can start the previous reasoning with questions: in which triplets does 1 appear, in which 2, and in which 3?

Evaluation. 1 point for determining the total amount of rods; 1 point for calculating the amount of rods per gardener; 2 points for listing all permissible triplets or corresponding notations; 1 point for each valid distribution option (i.e., 2 points for both options).