There are some ten digit numbers which when reversed and processed in a special way, something like this happens….
e.g. The number $4204234125$ in reverse is $5214324024$.
If we part the digits in the number $4204234125$ as $\{4,20,42,3,41,25\}$ and add them we get the sum which is equal to if we do the same with its reverse number $5214324024$ , namely $\{5,21,43,2,40,24\}$ and add these numbers with each other.
i.e. $$4+20+42+3+41+25 = 5+21+43+2+40+24$$
Another such ten digit number is $1223343322.$
How many such numbers exist? How to find them?
The partition must be like this: $1$ digit, $2$ digits, $2$ digits, $1$ digit, $2$
digits, $2$ digits.
Best Answer
Every ten digit number has this property.
Look at the digits in the partitioned sums in the example. The 4 ends up in the ones place of the 24. The 2 in the tens place of 20 ends up in the tens place of 24. The zero in the ones place of the 20 ends up in the ones place of the 40 and so on. Clearly the reversed partitioned sum would have the same value as the original partitioned sum.