The teacher wrote two numbers on the board one under the other and called Adam to add them. Adam correctly added them and wrote the result 39 under the given numbers. The teacher erased the topmost number, and the remaining two numbers formed a new addition problem. This time, the teacher wrote the correct result under the numbers, which was done by Bára. The teacher erased the topmost number again, and the newly formed addition problem was correctly solved by Čeněk, resulting in 96.

Determine the two numbers that were originally written on the board. 

(L. Šimůnek)
Let's represent all five numbers in the order they were written on the board (asterisks denote the currently unknown digits):

![](https://cdn.mathpix.com/cropped/2024_04_17_93ce04c5894139b12786g-1.jpg?height=243&width=80&top_left_y=918&top_left_x=994)

In the last solved addition problem $39+* *=96$, only one term is missing; the number on the 4th line is therefore $96-39=57$.

This gives us a similar situation in the example $* *+39=57$; the number on the 2nd line is therefore $57-39=18$. Similarly, we fill in the missing term in the first example: $39-18=21$.

The numbers originally written on the board were 21 and 18.

Scoring suggestion. 1 point for each unknown number; 2 points for the quality of the explanation; 1 point for a correctly formulated conclusion.