Data cube design: hard-to-aggregate measure

I'm in the process of designing the fact table for a data cube, and I have a measure which I don't really know how to correctly aggregate. The following SQL code will create a small sample fact table and dimension table:

create table FactTable (
    ID      int,
    Color   int,
    Flag    int)

insert into FactTable (ID, Color, Flag) values (1, 'RED',   1)
insert into FactTable (ID, Color, Flag) values (1, 'WHITE', 0)
insert into FactTable (ID, Color, Flag) values (1, 'BLUE',  1)
insert into FactTable (ID, Color, Flag) values (2, 'RED',   0)
insert into FactTable (ID, Color, Flag) values (2, 'WHITE', 0)
insert into FactTable (ID, Color, Flag) values (2, 'BLUE',  1)
insert into FactTable (ID, Color, Flag) values (3, 'RED',   1)
insert into FactTable (ID, Color, Flag) values (3, 'WHITE', 1)
insert into FactTable (ID, Color, Flag) values (3, 'BLUE',  1)

create table ColorDim (
    CID     int, 
    Color  int)

insert into ColorDim (CID, Color) values (1, 'RED')
insert into ColorDim (CID, Color) values (2, 'WHITE')
insert into ColorDim (CID, Color) values (3, 'BLUE')

FactTable and ColorDim are joined on FactTable.Color = ColorDim.Color. In the cube, there should be a measure called 'Patriotic' which counts object IDs including the colors red, white, or blue (at least one of the colors). The desired output is as follows:

When browsing the cube, if the user pulls in the Patriotic measure (pulling no dimensions), the total shown should be 2, since there are 2 IDs (namely, 1 and 3) which include at least one of the three colors. Notice that ID 1 should contribute 1 to the total Patriotic value, even though it has two of the colors.
If the user browses the Patriotic measure by the Color dimension, they should see a table like the following. Note that the the ID 1 contributes 1 to the RED count and 1 to the BLUE count.

+--------+-----------+
| Color | Patriotic |
+--------+-----------+
| RED | 2 |
| WHITE | 1 |
| BLUE | 2 |
+--------+-----------+

(I tried to create a table using this web app, but the spacing doesn't appear to be correct. Hopefully it's readable enough to understand.)

I'm sure this is a very basic cube design situation, but I haven't worked with cubes much before, and the measures I've used are usually simple SUMs of columns, or products of SUMs of columns, etc. Any help would be much appreciated.

(If it's relevant, I'm running the SQL queries which build the fact/dimension tables in MS SQL Server 2008, and I'll be designing the cube itself in MS Visual Studio 2008.)

Solution

I finally figured it out. First, I added one row per ID to the fact table containing pre-aggregated data for that ID, so the fact table becomes:

create table FactTable (
    ID      int,
    Color   int,
    Flag    int)

insert into FactTable (ID, Color, Flag) values (1, 'RED',   1)
insert into FactTable (ID, Color, Flag) values (1, 'WHITE', 0)
insert into FactTable (ID, Color, Flag) values (1, 'BLUE',  1)
insert into FactTable (ID, Color, Flag) values (1, 'PATRIOTIC',  1)
insert into FactTable (ID, Color, Flag) values (2, 'RED',   0)
insert into FactTable (ID, Color, Flag) values (2, 'WHITE', 0)
insert into FactTable (ID, Color, Flag) values (2, 'BLUE',  1)
insert into FactTable (ID, Color, Flag) values (2, 'PATRIOTIC',  1)
insert into FactTable (ID, Color, Flag) values (3, 'RED',   1)
insert into FactTable (ID, Color, Flag) values (3, 'WHITE', 1)
insert into FactTable (ID, Color, Flag) values (3, 'BLUE',  1)
insert into FactTable (ID, Color, Flag) values (3, 'PATRIOTIC',  1)

Similarly, add a row to the color dimension table:

create table ColorDim (
    CID     int, 
    Color  int)

insert into ColorDim (CID, Color) values (1, 'RED')
insert into ColorDim (CID, Color) values (2, 'WHITE')
insert into ColorDim (CID, Color) values (3, 'BLUE')
insert into ColorDim (CID, Color) values (4, 'PATRIOTIC')

Then, in MS Visual Studio, edit the DefaultMember property of the Color attribute in the Color Dimension as:

[Color Dimension].[ColorDim].&[PATRIOTIC]

The DefaultMember property tells MS Visual Studio that rows of the fact table which have Color 'PATRIOTIC' are already aggregates of the other rows with the same ID and other Color values.