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It is 1729. Discovered by mathemagician Srinivas Ramanujan, 1729 is said to be the magic number because it is the sole number which can be expressed as the sum of the cubes of two different sets of numbers.
If the single digit is 1 then the number is called a magic number. It is quite similar to the happy number. For example, 325 is a magic number because the sum of its digits (3+2+5) is 10, and again sum up the resultant (1+0), we get a single digit (1) as the result. Hence, the number 325 is a magic number.