A three digit (non leading zero) positive integer N is such that by adding 3 to N and dividing the result by 4 we obtain the reversal of N.
Determine the value of N.
Note: Computer program solutions are welcome but an analytical solution is preferred.
Let the digits of N ba a, b, c
Then
(1) 100a + 10b + c +3 =4*(100c + 10b +a)
c can only be 0, 1 or 2, in order that the RHS is not over 1002
and c must be odd in order that N is divisible by 4 after adding 3.
Therefore c = 1
Substituting and simplifying gives
(2) 32a - 10b = 132
Mod 10, a can only be 1 or 6, and 1 is too small.
So a = 6 and then b = 6
N = 661
Checking, (661 + 3)/4 = 166
Edited on May 13, 2023, 8:07 am
Analytical solution (spoiler)
