Create a list of divisors for each
48 : 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 48
36 : 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36
24 : 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24
Common divisors: 1 , 2 , 3 , 4 , 6 , 12
48/12 = 4 , 36/12 = 3 , 24/12 = 2
48/6 = 8 , 36/6 = 6 , 24/6 = 4
48/4 = 12 , 36/4 = 9 , 24/4 = 6
48/3 = 16 , 36/3 = 12 , 24/3 = 8
48/2 = 24 , 36/2 = 18 , 24/2 = 12
48/1 = 48 , 36/1 = 36 , 24/1 = 24
Just go with the largest divisor
AAAABBBCC
There are a lot of patterns you could make. 9 beads per section
9C4 * 5C3 * 2C2 =>
9! * 5! * 2! / (4! * 3! * 2! * (9 - 4)! * (5 - 3)! * (2 - 2)!) =>
9! * 5! * 2! / (4! * 3! * 2! * 5! * 2! * 0!) =>
9! / (4! * 3! * 2!) =>
9 * 8 * 7 * 6 * 5 * 4! / (4! * 6 * 2) =>
9 * 8 * 7 * 6 * 5 / (6 * 2) =>
9 * 8 * 7 * 5 / 2 =>
9 * 4 * 7 * 5 =>
63 * 20 =>
1260
There are 1260 different patterns that you could make. Have fun with that!