This problem involves logic-based math, I tried making truth tables for this problem but I don't think you can because there are 9 doors!
Below is what I came up with but I want to know if there is a better way of figuring this out.
Base on the tip from the hostess, there is something behind door8; then it is either 1 dollar or the price; since the sign on the price door is always true; therefore Door8 can only be false with \$1 behind it.
- Since door8 is false, then there is something behind door9. Similarly, door9 can only be false with \$1 behind it.
- Since door9 is false, door6 is true.
- Since door6 is true, door3 is wrong.
- Since door3 is wrong, then door5 is wrong, and door7 is true.
- Since door5 is wrong, door2 is wrong, and door4 is wrong.
- Since door7 is true, the Prize is behind door1.
- Since door2 is wrong, there is something behind door2; it is \$1 since the sign is false.
- Since door4 is wrong, the sign on door1 is true.
Base on the information above, we can create a table for all the doors.
Since sign on door one is true, and sign on door 6 is true, then there is nothing behind door 6 and 7.
Door 3/4/5 can be either \$1 or nothing.