The teacher wrote two numbers on the board one under the other and called Klára to add them. Klára correctly wrote the result under the given numbers. The teacher erased the topmost number, and the remaining two numbers formed a new addition problem. This time, Lukáš correctly wrote the result under the numbers. The teacher erased the topmost number again, and the newly formed addition problem was correctly solved by Magda, and the result was 94.

One of the two numbers that the teacher originally wrote on the board was 14, but we won't reveal which one. What could the other originally written number have been? Determine all possibilities.
The first number written on the board is denoted by $x$, the second by $y$. Klára wrote the sum

$$
x+y,
$$

Lukáš added

$$
y+(x+y)=x+2 y
$$

and finally, Magda added

$$
(x+y)+(x+2 y)=2 x+3 y .
$$

The value of the last mentioned sum is 94. The problem does not specify which of the unknowns $x$ and $y$ is 14, so we will consider both possibilities:

a) If $x=14$, then

$$
\begin{aligned}
2 \cdot 14+3 y & =94 \\
3 y & =66 \\
y & =22 .
\end{aligned}
$$

b) If $y=14$, then

$$
\begin{aligned}
2 x+3 \cdot 14 & =94, \\
2 x & =52, \\
x & =26 .
\end{aligned}
$$

At the beginning, the number on the board, besides 14, could have been 22 or 26.

Note. The two possibilities mentioned above can be considered at the very beginning. Then the sums that were written on the board in sequence are expressed as follows:
a) $14+y, 14+2 y$ and $28+3 y$, which leads to the equation $28+3 y=94$, whose solution is $y=22$.
b) $x+14, x+28$ and $2 x+42$, which leads to the equation $2 x+42=94$, whose solution is $x=26$.

Scoring suggestion. 1 point for each solution; 3 points for the quality and completeness of the explanation; 1 point for a correctly formulated conclusion.