Twisty Logic

Age 16 to 18
Challenge Level

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 ?