A string of 33 pearls has its largest and most valuable pearl in the middle. The other pearls are arranged so that their value decreases by $3000 \mathrm{Ft}$ per pearl towards one end and by $4500 \mathrm{Ft}$ per pearl towards the other end. How much is the middle pearl worth if the total value of the entire string of pearls is 25 times the value of the fourth pearl from the middle, on the more expensive side.
If the value of the middle bead is $x$ forints, then the value of the entire bead string, using the formula for the sum of an arithmetic sequence, is

$$
\begin{aligned}
x & +\frac{16}{2}[2(x-4500)-15 \cdot 4500]+\frac{16}{2}[2(x-3000)-15 \cdot 3000]= \\
& =x+16 x-2 \cdot 36000-15 \cdot 36600+16 x-2 \cdot 24000-15 \cdot 24000= \\
& =33 x-17(36000+24000)=33 x-17 \cdot 60000=33 x-1020000
\end{aligned}
$$

The value of the fourth bead on the more expensive side is

$$
(x-3000)-3 \cdot 3000=x-12000
$$

According to the problem,

$$
33 x-1020000=25(x-12000)
$$

which means

$$
8 x=1020000-300000=720000
$$

from which

$$
x=90000
$$

Ottó Zsidó (Pécs, Bányai P. Techn. III. o. t.)