# Machine learning to find fewest number of "puzzle pieces" that fullfill a certain requirement

Would machine learning be suitable for the following problem, and if so, what kind of learning?

I have numerous puzzle pieces, all having a value for identical properties. Example of one puzzle piece:

| $$Property$$ | Value |

| ---------- | ---------- |

| A | 10 |

| B | 300 |

| C | 21 |

| x_1 | 11 |

| x_2 | 17 |

| y | 33 |

Note that $$x_1$$ to $$x_2$$ gives the one-dimensional space that the puzzle piece would occupy on the x-axis.

The user can now specify $$A_{min},B_{min},B_{max},C_{min},C_{max}$$ , $$y_{total}, x_{min}, x_{max}$$

The problem to be solved is that I need to combine as few pieces as possible so that the puzzle pieces occupy the entire space between $$x_{min}$$ and $$x_{max}$$ (overlap allowed) while the sum of their $$y$$ values is larger than $$y_{min}$$.

As an additional constraint, all selected pieces need to have the identical $$A,B,C$$ values.

The output of the machine should be the $$A,B,C$$, $$x_1$$ and $$x_2$$ value of each piece that contributes to the solution and potentially a flag $$S$$ that is True if there is a solution and False if there is none.