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In this addition sum, each letter represents a different non-zero digit.

  $f$ $l$ $y$  
  $f$ $l$ $y$ +
  $f$ $l$ $y$ +
-- -- -- -- --
$a$ $w$ $a$ $y$  

What are the values of $a$, $f$, $l$, $w$ and $y$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
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