The first four digits are fixed (9, 9, 7, 9).

The remaining six digits should be such that it forms the least number possible of six digits, using only one digit twice.

Let’s use the digits in this way: the smaller digits will be used in left side [As the left side digits contributes more towards the value of the number: Any number, say, ”a_na_{n - 1}a_{n - 2….}a₁a₀ can be expanded as :

= a_n × 10ⁿ + a_{n - 1} × 10^{n - 1} + a_{n - 2} × 10^{n - 2} + a_{n - 3} × 10^{n - 3} + … + a₁ × 10¹ + a₀], and, 0 (the unique repeatable digit in this case) should be used twice as it is the smallest digit∷003568

[note, here the six digit number, unexpectedly starts with 0. Observe properly, this 0 actually lies in the middle of the actual ten digit number, which we are considering. So, no issue here.]

the smallest number is: 9979003568.