0Four digit number's summation after interchanging digits:
Let us take a 4-digit number represented as abcd.
The value of the number is obviously 1000a+100b+10c+d
By interchanging the digits such that the digits in thousandth, hundredth, tenth and unit's place is non-repetitive in each occasion,
We get,
bcda, cdab and dabc to be three other numbers.
Now, if we add all the four numbers, we get the value of the total as
1111(a+b+c+d).
Hence the summation is always a multiple of 11 and 101.
Example.:
Number 5368
By interchanging in the above pattern, we get 3586,8635,6853 whose summation is
24442 which is (101×242) and(11×2222).
