In the Kingdom of Dwarves, distances are measured in fairy miles (pm), fairy fathoms (ps), and fairy cubits (pl). At the entrance gate to the Kingdom of Dwarves, there is the following table for conversions between their units and ours:

- $1 \mathrm{pm}=3.85 \mathrm{~m}$,
- $1 \mathrm{ps}=105 \mathrm{~cm}$,
- $1 \mathrm{pl}=250 \mathrm{~mm}$.

King Dwarf I had the distance from the castle gate to the fairy lake remeasured. Three invited surveyors came up with the following results: the first reported $4 \mathrm{pm} 4 \mathrm{ps} 18 \mathrm{pl}$, the second $3 \mathrm{pm} 2 \mathrm{ps} 43 \mathrm{pl}$, and the third $6 \mathrm{pm} 1 \mathrm{ps} 1 \mathrm{pl}$. However, one of them made a mistake. What is the distance in meters from the castle gate to the fairy lake? By how many centimeters did the inaccurate surveyor err?

(M. Petrová)
First, let's convert the fairy tale units to centimeters:

$$
1 \mathrm{pm}=385 \mathrm{~cm}, 1 \mathrm{ps}=105 \mathrm{~cm}, 1 \mathrm{pl}=25 \mathrm{~cm} \text {. }
$$

Now we will express the distances measured by each surveyor in centimeters: the first surveyor measured $4 \mathrm{pm} 4 \mathrm{ps} 18 \mathrm{pl}$, i.e.,

$$
4 \cdot 385+4 \cdot 105+18 \cdot 25=1540+420+450=2410(\mathrm{~cm}) .
$$

The second surveyor measured $3 \mathrm{pm} 2 \mathrm{ps} 43 \mathrm{pl}$, i.e.,

$$
3 \cdot 385+2 \cdot 105+43 \cdot 25=1155+210+1075=2440(\mathrm{~cm}) .
$$

The third surveyor measured $6 \mathrm{pm} 1 \mathrm{ps} 1 \mathrm{pl}$, i.e.,

$$
6 \cdot 385+1 \cdot 105+1 \cdot 25=2310+105+25=2440(\mathrm{~cm}) .
$$

The distance from the castle gate to the fairy tale pond is $2440 \mathrm{~cm}=24.4 \mathrm{~m}$. The first surveyor was off by $2440-2410=30(\mathrm{~cm})$.