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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 $y$?

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*This problem is taken from the UKMT Mathematical Challenges.*

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