Let Xi=0 or 1xci = 1 indicate that I-colored balls have been drawn n times, and Xi=0 indicates that I-colored balls have not been drawn n times.

Let x be the number of colors of the ball drawn n times, and X=X 1+X2+...+X6.

P{Xi=0}=( 1- 1/6)^n

p{xi= 1}= 1-( 1- 1/6)^n

EX=EX 1+EX2+..+ex6=6[ 1-( 1- 1/6)^n]=6-5^n/6^(n- 1)

When EX=6, n can be estimated.