Filtering numbers according to certain ratios

I have a table to pick numbers according to their attributes. You can see the numbers and their attributes in the table. Each attribute is colored differently, and each attribute has a relevant filter box next to the table. In these filter boxes, I want to enter ratio numbers between 0 & 6, the total of which should be 6 only. I.e, 2,-4,4-2, 3-3, 6-0, 6-0, 5-1, 1-5. I have entered some example ratios in the worksheet.

Most of the attributes on the table have two filter boxes in the same color. The last attributes on the table have more than 2 filter boxes. Their ratio numbers are still between 0 & 6 and totaling 6 only. I have entered example ratios for these in the worksheet too.

The idea is to use as many of the filters to narrow down the numbers according to the ratios in the filter boxes. It is like multiple intersecting circles. I'm looking for a way to get and list the numbers left in the intersection.

Note: There might be cases where no numbers left when incompatible ratios are selected.
The data table and filter boxes can be seen on the worksheet below. I entered some example ratios and mocked up results.

I am not sure if this can be done with excel, but I'm open to any help I can get. Thanks in advance!
It'd be best to have an option to start the process after the ratios are entered.

Attachment 21610

Your goals are not easy to follow - but: you might like to try the 'solver' addin.
if this is not powerful enough, the Palisade software '@Risk' add in should do what you need

Thanks Werafa, I will check those out.