Twisty logic

Can you make sense of these logical contortions?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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 ?