Mysterious $10$-digit numbers, how many of such exist?
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.