That is an interesting page

Logic Level 2

I saw a page on the internet, which had these statements:

This page contains 1 False statement.

This page contains 2 False statements.

This page contains 3 False statements.

.

.

.

This Page contains 99 False statements.

This page contains 100 False statements.

If one of the above statements is correct. Then, it could possibly be the:

Can you catch some liars for me. Here are some of them who make statements worth deceiving

1^\text{st}

statement

{99}^\text{th}

statement

2^\text{nd}

statement Cannot be determined

{100}^\text{th}

statement This is an impossible scenario

1 solution

Chew-Seong Cheong
Jun 20, 2016

In this situation, there can only be one true statement, which means that the other 99 statements are false. Only the $\boxed{99^\text{th} \text{ statement}}$ is true.

But if the statement - "This page contains 99 false statements" is true, then all the statements except 100th statement becomes true as well, as there is no mention of "only" in any of the statements.

A Former Brilliant Member - 4 years, 10 months ago

Since there are 100 statements on the page, statement 99 "The page contains 99 false statements" means that only one statement (100-99) is true which is statement 99. So it is consistent.

Chew-Seong Cheong - 4 years, 10 months ago

That is an interesting page

Can you catch some liars for me. Here are some of them who make statements worth deceiving

1 solution

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