The digit in the hundred thousand places is both a square and a cube.
Only the digit in the hundreds place is larger than the digit in the ones place
Analyzing our choices:
since the tens place is a square, but cannot be larger than the ones place, it has to be either 1 or 4
the hundreds place is a cube which can be 8 not one since the digit in the hundred thousand places is both a square and a cube which is 1
also, the number is divisible by 5 meaning that the last digit must be 5 or zero. However, only the hundreds place is larger than the digit in the ones place so it must be 5
Looking at what we have so far:
1 _ _ 8 4 5
this number is divisible by 3 and cannot be larger than 5 which is in the units place
when a number is divisible by 3 all its digits must add to a number that is divisible by 3, meaning that the last unfilled digits can be filled by '0' and '3'
now the order of '0' and '3' is determined by whether the number is divisible by 7
