Find A & C in search results

I want to be able to add up to 10 tags to a record in a database (MongoDB), but I don't want to add 10 columns with the corresponding indexes for each of them. So I decided to add a unique amount of these tags.

eg. (with 6 tags)

|------------|
|value | tag |
|------------|
|1     |a    |
|2     |b    |
|4     |c    |
|8     |d    |
|16    |e    |
|32    |f    |
|------------|

eg.

a + b = 3

b + c + d = 14

Then I save only the sum of the value in Mongo.

These combinations are always unique, and I can "restore" them back to tags when retrieving from persistent storage using iteration.

int tagSum
for each (tag in tagCollection.OrderDescending)
{
    if (tagSum >= (int)tag)
    {
        TagProperty.Add(targetAge);
        tagSum -= (int)tag;
    }
}

However, my problem is that I thought there should be a mathematical formula that I could use to request a specific tag, for example. find "c tag" by passing the value 4. I am either mistaken or cannot find it.

Multikeys Mongo, , 1 10