"There is another way of coming to this conclusion without
the effort of going through a spread sheet, based on finding who
tells the truth first.
"We know that there are 10 correct statements, since they don't
say the same number of lies. If the statements are clustered into
possible groups we come into 9 possible groups. They are as follows:
1- Group 1, who ate the apple, out of 6 different statements said,
1 or 2 are correct. (2 if the case 'snake ate the apple' is true
because it was said twice).
2- The snake is in the garden; out of 2 statements only 1 can be
3- Eve weeded the garden; again 1 out of 2 can be correct
4- Abel did his chores; 1 out of 2
5- 'We are not equally truthful' is definitely true so it is 1
out of 1 possibly correct
6- The snake lies; 1 out of 2 possible statements
7- Abel does not always tell the truth; it is said once and is
8- Eve prefers Abel; out of 2 statements only one is right.
9- Snake can't look over the hedge; either 2 correct or 2 false.
If we add up the possibilities of all the clusters except the
last (snake looks over the hedge) we come up with a maximum of
8 or 9 possible true statements, which falls short of the required
10. Therefore, not only do we know that snake cannout look over
the hedge, but that also snake can't possibly have eaten the apple,
or else it would yield 11 true statements.
I guess I would have to again say that this is not how I started
the first solution, but I guess I came up with it as I re-thought
of a different approach.
Regarding posting the solution, it might be a good idea. You
can put possibly correct and distinct solutions there too.