I'm not the best at math, but I took every individual gem in the picture(fusions separated) equaling 40 gems. Multiplied it by 39 since I didn't want duplicates. Totaling 1,560 combinations consisting of just two gems. To figure out three gem combinations After that I went down the line multiplying 1,560 by 39 subtracted by 2(taking into account duplicates such as fusions consisting of just 3 aquamarine, and fusions consisting of two sapphires, and a ruby). Totaling 57,720 fusions consisting of three gems. Each time taking the remainder, and multiplying it by the subtracted equalizer.Four gem fusions - 57,720X(37-3)=1,962,480Five gem fusions - 1,962,480X(34-4)=58,874,400six gem fusions - 58,874,400X(30-5)=1,471,860,000I did however check my math using a combination generator textmechanic.com/text-tools/co… input 40, selected combinations of 2, and turned off duplicates. With my answer 1,560 being correct. My math from there on I'll admit was incorrect. As the number of three gem fusions totaled to 59,280.Four gem fusions - 2,193,360five gem fusions - 78,960,960six gem fusions - 2,763,633,600Though my hasty math was semi-close, and beats counting them out by hand in the long run.