Pip is building model car racing tracks using a large supply of the two types of square plate shown. Ignoring the tabs and slots where plates are snapped together, both types measure 20cm x 20cm. In the first type, the track is a straight line joining the middles of opposite sides. In the seconds, the track is a quarter circle joining the middle of adjacent sides. Plates can be snapped together in any orientation, as long as the track is continuous. Pip wants to complete the track shown below but, because there is limited space, additional plates can only be put in the 4 x 4 grid indicated by dotted lines. 1. Explain why, no matter how the circuit is completed, Pip must place an even number of additional curved plates. 2. Explain why, no matter how the circuit is completed, Pip must place an odd number of additional straight plates.

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