Handsome numbers (numbers which have a pandigital partition)

A number is said to be handsome if it has a pandigital partition, that is, a partition in which each of the ten digits is used precisely once among the parts.

The smallest handsome number is, therefore, 54 = 10+2+3+4+5+6+7+8+9

Is 2025 handsome? And if so, how handsome is it, i.e., how many pandigital partitions does it have?

You can solve the problem via integer linear programming as follows. For each of the 1249 candidate parts $p\in P$ with no repeated digit, let $D_p$ be the set of digits, and let binary decision variable $x_p$ indicate whether part $p$ is used. The constraints are \begin{align} \sum_{p\in P} p x_p &= 2025 \tag1\label1 \\ \sum_{p\in P: d\in D_p} x_p &= 1 &&\text{for $d\in\{0,1,\dots,9\}$} \tag2\label2 \end{align} Constraint \eqref{1} partitions $2025$. Constraint \eqref{2} uses each digit $d$ exactly once.

It turns out that there are

5324

solutions, of which

7 + 594 + 623 + 801

and

3 + 4 + 5 + 6 + 20 + 1987

illustrate the range of the largest part.

Partial answer:

Is 2025 handsome?