Evička had a set of nine building blocks, which were marked with the numbers $1, 2, 3, 4, 5, 6, 7, 8$, and 9. Over time, she managed to lose all the pieces in the following way:

- first, she lost four pieces marked with odd digits,
- then she lost pieces with the product of the digits being 24,
- finally, she lost the last two pieces, which had even digits.

Determine which digits could have been written on the last two pieces. Find two solutions.

(E. Novotná)
Among the given numbers, there are five odd numbers and four even numbers. After losing four odd numbers, Evička was left with one odd number and all four even numbers $(2,4,6,8)$. Since 24 is not a multiple of 5, 7, or 9, but is a multiple of 1 and 3, the remaining odd number could have been either 1 or 3.

After losing the pieces with a product of 24, only two even numbers remained. This product must therefore have been expressed using one odd number (either 1 or 3) and two even numbers (chosen from $2,4,6$ and 8). This is possible either as $24=1 \cdot 4 \cdot 6$, or as $24=3 \cdot 2 \cdot 4$. In the first case, the numbers on the last two pieces would be 2 and 8, and in the second case, they would be 6 and 8.

Evaluation. 2 points for determining that the remaining odd number was either 1 or 3; 2 points for determining that 24 should be the product of one odd and two even numbers; 2 points for analyzing the possibilities and drawing a conclusion.

If the solver first considers all possible products such as $24=3 \cdot 8=1 \cdot 3 \cdot 8$ etc., and then selects the valid options, it must be clear from the comments why they are valid. For a solution without justification, award no more than 2 points.