Copyright © University of Cambridge. All rights reserved.

## 'Weekly Challenge 15: Indexing Problems' printed from http://nrich.maths.org/

Constructing a really clear argument to this problem can be
difficult!

Put simply:

Suppose that exactly one of the following statements is true:

A: Ultra Ref does refer to itself in its index

B: Ultra-Ref does not refer to itself in its index

Look at each in turn:

IF (Ultra-Ref does refer to itself in its index) THEN (Ultra-Ref
does not refer to itself in its index)

IF (Ultra-Ref does not refer to itself in its index) THEN
(Ultra-Ref does refer to itself in its index)

In both cases, our supposition is contradicted and Ultra-Ref is
therefore a logical impossibility.