Vojta bought 24 identical square tiles. The side of each tile measured $40 \mathrm{~cm}$. Vojta wanted to create a rectangular platform in front of the cottage with the smallest possible perimeter. How many meters did the perimeter of the paved rectangle measure, given that no tiles were left over? Vojta did not cut or break any tiles in any way.

(L. Hozová)
Let's go through all the possibilities; for each, we will provide the dimensions of such a rectangle in "tiles" and further the perimeter in "tiles," resp. in "sides of tiles":

- dimensions: $1 \times 24$, perimeter: $2 \cdot(1+24)=50$,
- dimensions: $2 \times 12$, perimeter: $2 \cdot(2+12)=28$,
- dimensions: $3 \times 8$, perimeter: $2 \cdot(3+8)=22$,
- dimensions: $4 \times 6$, perimeter: $2 \cdot(4+6)=20$.

It is clear that the smallest perimeter expressed in centimeters/meters must also be the smallest when expressed in "tiles." The smallest perimeter is obtained in the fourth case, which is 20 tiles. If the side of one tile is $40 \mathrm{~cm}$ long, then 20 such sides measure a total of $20 \cdot 40=800(\mathrm{~cm})$. The perimeter of the paved rectangle measured 8 meters.

Evaluation. 1 point for the idea of the solution; 1 point for each correctly stated and analyzed possibility; 1 point for the result.

If the solver does not list all possibilities and does not explain why some of them were omitted (e.g., in the first possibility, that the perimeter is too long compared to the other perimeters), they can receive a maximum of 4 points, even if they provide the correct result.