Find A & C In Search Result - mongodb

Question

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 related indexes on each of them. So I thought I'd add the unique sum of these tags.
e.g. (with 6 tags)
|------------|
|value | tag |
|------------|
|1 |a |
|2 |b |
|4 |c |
|8 |d |
|16 |e |
|32 |f |
|------------|
e.g.
a + b = 3
b + c + d = 14
I then store just the sum of the value in Mongo.
These combinations are always unique and I can "reconstitute" them back into tags when pulled from persistent storage using iteration.
int tagSum
for each (tag in tagCollection.OrderDescending)
{
if (tagSum >= (int)tag)
{
TagProperty.Add(targetAge);
tagSum -= (int)tag;
}
}
My problem however is that I thought there must be a mathematical formula that I could use to query for a specific tag e.g. find the "c tag" by passing in the value 4. I'm either wrong or I cannot find it.
I'm happy to go with the Multikeys solution in Mongo but I have a lot of other data to index and using 1 index instead of 10 would just be nicer‽

Answer 1

Multikeys is the right approach to this problem as it can find any document from the single index on the array without a table-scan. In your case you can just put the appropriate selection of letters representing the tags into the array: ["a", "d", "e"].
In more complicated cases where each field could contain the same tag values, for example song names, album names, artist names, ... I sometimes add the tag phrase twice: once on its own and once with the field name pre-pended, e.g. "artist:Hello". Now I can search on the tag word occurring in any field OR the tag word occurring in a specific field and either way it will use the index to find matching records.

Answer 2

Convert the tags a-f to an integer 0-5, call it tagValue, then the number you want is 1<<tagValue.