The value of a three digit number increases by 108 when the first digit is palced at
the last and the value of the number increases by 189 when the last number is
placed at the first. Determine the summation of all the possibls numbers.
I'm assuming that the 1st and last digits are not swapped, but that the others are shifted to make room.
If the digits are h,t,u for hundreds, tens, units, then we are told that
100t+10u+h = 100h+10t+u + 108
100u+10h+t = 100h+10t+u + 189
or,
99h-90t-9u = -108
90h+9t-99u = -189
t = h+1
u = h+2
Since all digits must be between 0 and 9, that means we have the possibilities
789
678
567
456
345
234
123