There are 6 boxes on the table. According the host: Three are empty ($0). One has $1000, not a bad prize. The fifth has $100,000 and the last has 1 million dollars.
The boxes are A,B,C,D,E and F. You dont know which check (or no check in the case of the empty boxes) is in which box. You do know, however, that E has less than $100,000.
You have the option of selecting 3 boxes and are told how many empty boxes are present in those three boxes. Then you have the option again, for any 3 boxes.
Since it doesn't matter, you choose A, B and C for the first choosing. You are told there are two empty boxes there. For the next pick you choose B, C and D. At the same time, the host takes pity and takes away box F, showing the $1000 check inside, and throws it away. Only ABCD and E remain. You repeat your desire to learn how many empty boxes are among B, C and D. The host says the number, and after a quick thought, you pick a box. The host opens it, showing you a check for $1,000,000.00!
What number did the host say, and what went through your mind?