Let us begin with these pieces:
- The number is less than the # of years in a century...
- There are 2 digits in the whole part..
- There are 5 digits all together...
- The number is greater than 5 dozen...
From this given, we can establish that:
Now, let us translate the rest of the given into algebraic terms:
1. Now, step number 1: solve simultaneously:
2. Now solve simultaneously again with:
3. Then, let us examine the given:
It is obvious to see that d = 0. It is impossible that c = 0 since the product of c and e is 24. This is the key; plug in the relations we got previously:
If c = 6, then e = 4 but this doesn't satisfy the inequality
Therefore, c = 4 and e = 6