Tentukan banyaknya tripel bilangan asli (x,y,z) sehingga : 1 ≤ x < y + 2 < z + 4 ≤ 12

banyak z yang bisa diisi: 1,2,3,4,5,6,7,8

jika z = 1, y = 1,2,
jika z = 2, y = 1,2,3,
jika z = 8, y = 1,2,3,....,9

jika y = 1, x = 1,2
jika y = 2, x = 1,2,3
jika y = 9, x = 1,2,3,....,10

banyak bilangan tripel (x,y,z) sama saja dengan banyak kombinasi bilangan z yang bisa diisi ketika y = .... dan x = .....

1 2 3 4 5 6 7 8 9 (y)

8 8 7 6 5 4 3 2 1 (x = 1)
8 8 7 6 5 4 3 2 1(x = 2)
...8 7 6 5 4 3 2 1 (x = 3)
......7 6 5 4 3 2 1 (x = 4)
.........6 5 4 3 2 1 (x = 5)
............5 4 3 2 1 (x = 6)
...............4 3 2 1 (x = 7)
..................3 2 1 (x = 8)
.....................2 1 (x = 9)
........................1 (x = 10)


Jumlah z =
16 + 24 + 28 + 30 + 30 + 28 + 24 + 18 + 10 = 208 bilangan