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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.

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