Muenchhausen Numbers

December 6, 2019

A radix-10 number is a Muenchhausen number if it is equal to the sum of its digits, each digit raised to the power of itself. For instance, 3435 is a Muenchhausen number because 3**3 + 4**4 + 3**3 + 5**5 = 3435. Strict Muenchhausen numbers do not permit 0 as a digit, because 0**0 is undefined. Variant Muenchhausen numbers permit 0 as a digit, with 0**0 defined as 0. Muenchhausen numbers also exist with radices other than 10.

Your task is to find all the Muenchhausen numbers in radix-10. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.


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