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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