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Sunday Puzzle-47

User Rating: / 9
Written by Administrator   
Sunday, 28 July 2013
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

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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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Comments (1)
1. Written by O_x on 07:01 29 2013 .
This shouldnt be a big problem for blindfold chess players or anyone interested in blindfold chess... besides having common sense. 
Its not that easy for me though... :p 
Imagine a 4x4 tiny chessboard; where we have only a-d columns and 1-4 rows.The trick lies on how the 4 random tiles should be chosen. 
If we start from b1 and choose the next square d2(following a knight's move), then c4 ...and finally a3, wed have followed exactly what the question says. 
Similarly, starting from c1 we can have 4 correct squares: c1, d3, b4 and a2. So,there are only 2 possible groups of 4 squares. 
Looking at the 5 directions, the magic tile has to be one of the 4 centre squares: b2, b3, c2 or c3. 
Now we can simply reverse the given directions from the centre squares and follow them one by one to reach 3 of the 4 chosen squares. 
Only one of the centre squares can lead us to 3 correct squares... 
The MAGIC TILE is b3.  

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