Solver for Channel 4 Countdown's number

The game has the option or you to choose six numbers, up to 4 can be big numbers. Big numbers are 25, 50 75, 100 and the rest can be any number between 1 and 10. Using the six numbers without repetition, you have to reach the target, which is a 3-digit number. Only simple operations like are allowed and results can't be fractions.

The backend solver only needs the input of how many big numbers need to be chosen and the numbers will be generated at random and the target can be set at random. The solver will provide an answer with the least number of steps used.
Currently the GUI is only implemented to to take user-defined input, intended to be used to play along with the show.
in future updates, options to generated random numbers without user input will be added.