X means throwing once. When throwing any of 1, 2 and 3, it is marked as X= 1, otherwise it is marked as X=0.

Use Sn to represent n times, sn = x 1+x2+...xn.

Make sure that any point in 1, 2 and 3 appears, that is, find Sn >；; The probability of 0 is guaranteed to be 99.9999%

Mathematical expectation e (sn) = ex1+ex2+... exn = 0.5+0.5++...+0.5 = 0.5n.

Variance var (sn) = var (x1)+var (x2)+...+var (xn) = 0.25n.

Central limit theorem;

0.25n under (Sn-0.5n)/ radical sign obeys the standard orthogonal distribution.

Probability p (sn > 0)=P((Sn-0.5n)/ 0.25n > under the root sign >; (under root number 0 -0.5n/ 0.25n) = p (under root number (sn-0.5n)/0.25n >:-0.5n/0.25n) = 1-p ((sn-0.5n)/0.25n < =-0.

That is to say, the probability that the standard orthogonal normal distribution is less than or equal to 0.5n/ root sign is 0.25n. The 99.9999% corresponding quantile of the standard orthogonal distribution table is 4.68, so 0.25n > 0.5n/ root sign; =4.68

So the root number n & gt=4.68.

n & gt=2 1.9024

Throw it at least 22 times