Puzzle courtesy of Barry R. Clarke, columnist for The Daily Telegraph and international puzzle expert
Check out his new book "Mathematical Puzzles and Curiosities" on Amazon

The Mermaid's Wish

One day, as Popkin was mopping his bathroom floor, he wished that life could be so much easier. Suddenly, a mermaid appeared in the mop bucket.

   "Life can be easier", said the mermaid, "whenever you wish it to be. All you have to do is stand on the magic tile when you make your wish. Then any wish you make will be granted".

   Now Popkin's bathroom floor consisted of 16 square tiles arranged in a 4x4 square and, apparently, one of them was the magic one. The mermaid gave Popkin his instructions for finding it. He must choose exactly four tiles so that no row nor column was used more than once and no two tiles were diagonally adjacent. Then Popkin must stand on one of his chosen four and follow only one of the following five directions.

  (1) Walk two tiles to the left.

  (2) Walk one tile up.

  (3) Walk one tile down.

  (4) Walk two tiles to the right.

  (5) Walk one tile up then one tile to the right.

Popkin should then be standing on the correct tile. Exactly three of the chosen four tiles should lead to the magic tile (with a different direction for each of the three).

   Where was the magic tile?

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