perplexus.info :: Logic : Only one untrue statement

Only one untrue statement (Posted on 2013-07-18)

Yesterday he told me:
"....1.Tomorrow is not Sunday.
2. Neither it was yesterday.
3.Day after tomorrow is neither Saturday nor Sunday.
4.Yesterday it was neither Monday nor Wednesday.
5.The day before yesterday was not a Wednesday and tomorrow will not be Tuesday.
6.And Today is not Wednesday as well..."

What day of the week is to-day?

See The Solution Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

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Some analysis

| Comment 3 of 10 |

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

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