(1) A: The first time: 1/3 of the whole cake.

B: The first time: 2/3 * 1/2 = 1/3 of the whole cake, and there is 1/3 left in the cake.

A: The second time:1/3 *1/3 =1/9.

B: The second time: (1/3-1/9) *1/2 =1/9, and the rest of the cake is 1/3-2/9= 1/9.

..... and so on. A * * * cut1/3+1/9+1/27+1/81= 40/81.

The same is true of B 40/8 1

(2) So the cake also has1-80/81=1/81.

2. The original 1/2 was left for the first time.

Pour out the remaining 1/2 for the second time and then1/2 * 1/3 =1/6 * * is 2/3, so there is still1/3 left.