Determine the years of our century that exhibit the following property of their digits. Subtract the first digit from the second, the second from the third, and the third from the fourth, and form an arithmetic progression with these three differences.
The sought year is of the form:

$$
1800+10 x+y
$$

and the conditional equations are these:

$$
\begin{gathered}
8-1=7 \\
x-8=7+d \\
y-x=7+2 d
\end{gathered}
$$

From equation 2),

$$
x=15+d
$$

Substituting this into equation 3), we get:

$$
y=22+3 d
$$

Calculating the difference from equation 4),

$$
d=x-15
$$

Similarly, from equation 5),

$$
d=\frac{y-22}{3}
$$

Comparing these two values of $d$, we get:

$$
3 x-23=y
$$

From this indeterminate equation, considering the nature of the problem, only the following values can be used:

$$
\begin{gathered}
x=8, y=1 \text { and } \\
x=9, y=4
\end{gathered}
$$

Thus, the two years are 1881 and 1894.

The student of the 6th A class of the Budapest II. district high school.

The problem was also solved by: Jahl Jenö, 7th class, II. district high school, Budapest.