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## 'Road Maker 2' printed from http://nrich.maths.org/

This problem follows on
from Road Maker, where the rules of making roads are
detailed in full.
The Munchkin road making authority have commissioned you to work
out the possible destinations for their roads. Use
Cartesian coordinates where the first tile is placed with opposite
corners on $(0,0)$ and $(1,1)$.

Investigate ways in which you can reach your destination. You
may like to consider these questions:

- Can you make roads with rational values for the $x$ coordinate
of the destination?
- Can you make roads with rational values for the $y$ coordinate
of the destination?
- Can you create a road with the $x$ coordinate equal to any
integer multiple of one half?
- Can you make roads for which the coordinates of the destination
are both rational? Both irrational?
- Can multiple roads lead to the same destination? For which
destinations is the road unique?

You might like to experiment with this interactivity

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