# [Jelly], <s>26</s> 25 bytes

    2ṗ⁵’µ×“wØ][:koR¶{‘^/=µÐfḢ

[Try it online!][TIO-j3ky2rp4]

Takes input as a 7-bit integer. Returns the binary form of a 10-bit integer.

This just brute forces all possibilities. Remove the `Ḣ` to get all possible outputs or replace it with an `X` to get a random possible output.

[Magic Visualization Program!](https://tio.run/##y0rNyan8/3B396OGOY8adz3c0ftw18KHO7Y93NX5cEfziXUPd3U/3DnzUcOMeEMjA64soCoFGHjUMPfQ1qN7Dk90O7T10LpMVaNDW@25LA8tPrT18HSvRw0gTYcnpB3aCtYTDVRtbQ1kxtraQbU@alrDVWxuxHVos7ahkYXTwx1d4VxGZkcn24MNOLrHwUDHwA3isvia@BogAunjOjnZ8Mh@nYc7WuL0YfoOb4g53A40rthYBUhGHVppdGQ/kGECJqMiI7mQHWTtYHpk/@H2/0YPd05/1Ah03UyQfUBLyg/PiI22ys4POrStGqg0Tt/20Gag1IS0hzsW/Qf6y@LI/v//DS0A "Jelly – Try It Online")

###How it works 
    2ṗ⁵’µ×“wØ][:koR¶{‘^/=µÐfḢ  - main link, takes one integer
    2ṗ⁵’                       - generate all length-10 binary arrays
        µ                µÐf   - now we find those arrays which correspond to digit-
                                  sequences which work to switch off all segments:
                                  Filter (keep) those arrays which:
         ×                      - multiplied by 
          “wØ][:koR¶{‘          - [119, 18, 93, 91, 58, 107, 111, 82, 127, 123] 
                                   (encoding for turned-on segments given number)
                      ^/        - reduced by XOR
                        =      - are equal to (implicit) the program's input
                            Ḣ  - output the first of these valid arrays
                                     


[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-j3ky2rp4]: https://tio.run/##AUAAv/9qZWxsef//MuG5l@KBteKAmcOww5figJx3w5hdWzprb1LCtnvigJheLz3DsMOQZuG4ov///zE49W5vLWNhY2hl "Jelly – Try It Online"