Special Integers - The Setup

to make sure all digits are distinct, you must remember which digits you've already placed. A digit can only appear once. How do you track "used digits"? A bitmask.

If bit $d$ is set, digit $d$ has been used. Ten digits means a 10-bit mask. When placing digit $d$, check if bit $d$ is already set. If yes, skip. If no, set bit $d$ and continue. Take time to understand the problem structure. The recursive relationship often becomes clear once you see how smaller instances relate to larger ones.