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Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

The two shaded squares are those on which the block began. After the first move, it occupies the squares labelled $1$ (or $1/5$). After the second move, it occupies the squares labelled $2$ and so on. After the fifth and final move, it occupies the squares labelled $5$ (or $1/5$). As can be seen, $19$ squares have been occupied altogether.
Blockboard solution

This problem is taken from the UKMT Mathematical Challenges.