1. 1 shilling (12 pence)
Joe can’t be telling the truth because then Beth would be lying, and Al’s statement (which is also a lie) would mean that Beth is telling the truth. These two facts contradict each other. Therefore Joe is lying, which means that Beth is telling the truth.
4. 11 times
7. 13 days
8. In order, left to right: Green, red, light blue, brown
9. 1 in 3
For any woman to have two children of different ages, the four equally likely outcomes are:
Older boy, younger girl
Older girl, younger boy
However, if you know that at least one of the children is a girl, that eliminates “two boys” and leaves only three equally likely outcomes, one of which is “two girls”.
10. The Green Door.
Assume Freedom is behind the red door. All three doors would then have true statements which we know is not possible since one of them must be false.
Assume Freedom is behind the blue door. All three doors would then have false statements which we know is not possible since one of them must be true.
Freedom is therefore behind the green door. The blue door and the green door have true statements and the red door has a false statement.