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## 'Twisty Logic' printed from http://nrich.maths.org/

Sometimes mathematical setups
which appear to be straightforward can lead to circular of
self-contradictory or 'paradoxial' logic. Give your brain a workout
by thinking about these scenarios .

The Surprise Test

A teacher tells her class that there will be a test given on one
afternoon next week. She also tells them that they will not know
which day until they are told on the morning of the test.

Can this test be given on
Friday ? Can it be given
on any other day ?

The universal reference
book

Consider a very big book, UltraRef, which refers in its index to
every book which does not refer to itself in its index.

Does UltraRef refer to itself in
its index?

Smallest number paradox

Let a number N be defined to be ''The smallest whole number not
definable in under eleven words''

Can N be defined in this
way ?

The liar

My friend said ''I only ever lie''.

Was he telling the truth
?

The false sentence

Consider the sentence "This sentence is false"

Is the sentence true or
false ?

The erroneous statement

Consider the statement "There are tthree errorss in this
statement"

Is the statement true
?