3.42 The digits of a certain three-digit number form a geometric progression. If in this number the digits of the hundreds and units are swapped, the new three-digit number will be 594 less than the desired one. If, however, in the desired number the digit of the hundreds is erased and the digits of the resulting two-digit number are rearranged, the new two-digit number will be 18 less than the number expressed by the last two digits of the desired number. Find the original number.
3.42 The desired number has the form $100 x+10 y+z$, where $x, y, z$ form a geometric progression, i.e.

$x z=y^{2}$.

According to the condition, we have:

$100 z+10 y+x=100 x+10 y+z-594$, from which

$x-z=6$

$10 y+z=10 z+y+18$, from which

$y-z=2$.

The system of equations (1), (2), (3) is satisfied by $x=8$, $\boldsymbol{y}=4, z=2$. The desired number is 842.

Answer: 842.