1729 is a Magic Number

Why 1729 is a magic number? Answer Logically.




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In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
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My hundreds digit is eight less than my tens digit.
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What number comes next in the series?

5 15 5 18 5 24 14 20 _

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In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki