# MAT - Paper 2009 - Q5

> Source: https://ollybritton.com/notes/maths/problems/mat/2009/q5/ · Updated: 2021-10-14 · Tags: mat, notes, maths

## Flashcards
### 2021-10-14
##### ![PHOTO TOUR](tour.png) For a journey where you get back to the beginning (a "tour"), what must be true about every move made??
It must have a corresponding opposite; i.e. a forward must have a backward and an up must have a down.

##### ![PHOTO TOUR](tour.png) If every move has to have an opposite for a tour, why are $n \times n$ where $n$ is odd not possible??
There must be an odd total number of moves $n^2$ and it's impossible for an odd number to come in pairs.

##### ![PHOTO TOUR](tour.png) When thinking about traversal questions like this one, what is it good to consider??
If moves must come in pairs, or there is some relation between current moves and future ones.

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