We can translate each of the statements as follows:
1. It is not Saturday
2. It is not Monday
3. It is not Thursday and it is not Friday
4. It is not Tuesday and it is not Thursday
5. It is not Monday and it is not Friday
6. It is not Wednesday
As Kenny M states, this leaves the only possibility as Sunday, so "today" must be Monday.
However, the title implies one (and only one) of the (numbered) statements is false. We can narrow this down:
2 cannot be false, as it would make 5 false as well.
3 cannot be false, as it would make one of 4 and 5 false.
5 cannot be false, as it would make one of 2 and 3 false.
This leaves the possibilities of it being Saturday (1 is false), Tuesday (4 is false), or Wednesday (6 is false). "Today" could be Sunday, Wednesday, or Thursday.
I cannot see how to narrow it down further, unless I'm misinterpreting the statements. Could "it" be referring to something else? For example, could 4 mean "Yesterday [the day after tomorrow] was neither Monday nor Wednesday"?
Posted by snark
on 2013-07-18 20:35:04