Suppose, the number of one of the houses is “xy”, whose numerical value = (10x + y).
So, the number of the other house is “yx”, whose numerical value = (10y + x).
Let, “xy” > “yx”.
Now, difference of house numbers = {(10x + y) - (10y + x)} = {9 * (x - y)}; so the difference is a multiple of 9.
Now, the smallest positive number, divisible by 9, that ends with 2 is 72 = (9 * 8).
So, (x - y) = 8.
Since, 0 ≤ x, y ≤ 9; so, there are two solutions in hand:
I) x = 8, y = 0……………………..this makes the house numbers: “80” and “08”.
II) x = 9, y = 1…………………..this makes the house numbers: “91” and “19”.
So, the lowest possible numbers of the houses are “80” and “8” (not “91” and “19”).
A single digit number can not have its reverse number. hence 10,20,30,40,50,60,70,80 and 90 can not be the house number
Reverse of these numbers is same, hence 11,22,33,44,55,66,77,88 and 99 can not be the house number
For other reverse numbers the difference will be in multiples of 9 like 9,18,27,36,45,54,63,72,81
As the difference between house numbers ends in two, the lowest possible numbers of our house are 19 and 91
When 0 (zero) also considred as part of house number, the lowest possible numbers of our house are 08 and 80
