How to know which checkbox are selected if I have a number with the sum of all values checked?

I have an existing database, and my table has a field in which is stored a value, a sum of all "values" of my checkbox list.

Another programmer made this method, called it "logic sum". I don't know this method, but now I need to know the reverse method, so I can know which checkboxes are selected by using the Sum value of all their values.

I really don't know how to do this ... I am using C# with asp.net, but the logic should to be the same for all languages.

Can you help me?