2020/026) Call a 3-digit number geometric if it has 3 distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest geometric number.

 Let the common ratio of the digits of smallest number be x.

The smallest digit is 1 and largest digit is 9 and the ratio of them is 9 which is $3^2$

So we have a number 139 starting with 1 and let us check if can have a smaller number than this. if take the ratio 2 then we get a smaller number 124.
Now that larger number is 931 with the common ratio with $\frac{1}{3}$ and as we do not have a factor of 9 more than 3( excluding 9 it self) the largest number is 931.
So the difference is $931-124= 807$