After reading your answers i just figured the there is no 3rd way of solving this because the 2nd and 3rd methods are almost identically
So the quest has now ended : the winner are Shadow seeker and Kafuuka
The solutions were
Shadow Seeker
We know 6x+933=Y
And that if we write the number as WYXZ that W-Z=7
Since it is 6 times higher that the reverse, Z has to be 1 and W 8
Otherwise the equation would make no sense.
We're dealing with numbers out of N, so only these work, although theoretically 7 and 0 work as well. The issue with 6x (lower than 1k)+ lower than 1 k is that it won't reach 7 k, so we know it's 8 and 1, since 2 *6 isn't anywhere close to 9 and exceeding the limits.
The next step is the missing two numbers from the mid, all you need is just a little testing with the numbers you input 97, 86, etc and go down using a calculator: everything that divided by it's reverse gets 6 is marked and then you just check which is the right one.
Solution:
8421
and Kafuuka's
a * 1000 + b * 100 * c * 10 + d - 933 = 6* ( a + b *10 + c *100 + d *1000 )
|a - d|= 7
|b - c|= 2
994 a + 40 b - 590 c - 5999 d = 933
from this we can guess a should be larger then d, thus a = d + 7
trying b = c +2 or c - 2:
994 ( d +7) + 40 ( c +? 2) - 590 c - 5999 d = 933
- 5005 d - 550 c = - 6105 +160?
d = 1
c = 2
a = 8
b = 4
8421 - 933 / 1248 = 6