Each of the seven colors on the cards has its own number.

Tiny color threads going through all the seven beads in each necklace have their numbers as follows:

Red - 1; Orange - 2; Yellow - 4; Green - 8; Light Blue - 16; Blue - 32 and Violet - 64. They use a binary code.

The colors on the beads are numbered as follows:
Red - 1; Orange - 2; Yellow - 3; Green - 4; Light Blue - 5; Blue - 6 and Violet - 7.

All the colors form a rainbow spectrum, so this makes them and their order in both sequences easy to memorize.

When you look at the cards which remain unturned you simply have to count (as quick as you can) the sum of the colors of threads on these cards. You always get a two-digit number which says you the two colors of the chosen bead. 

For example, your see that three threads - Orange, Green and Blue lie opened. They give you 2+8+32=42. This means that the center of the chosen bead has the 4th color (Green), while its border has the 2nd color (Orange). 

To demonstrate this trick smoothly you may want to have some practice, however.