Munchausen Number

Posted: 30 Jan 2011 06:44 AM PST

Munchausen Number is a number that is equal to the sum of its digits each raised to a power equal to the digit.

Munchausen number is also called perfect digit-to-digit invariant (PDDI) because of the above feature.

The only Munchausen numbers are 1 and 3435.

Specialty of 3435 -

3³ + 4⁴ + 3³ + 5⁵ = 27 + 256 + 27 + 3125 = 3435

though, 0⁰ is undefined but if we consider it as 0, then there is one more Munchausen number founded till date - that number is 438579088

4⁴ + 3³ + 8⁸ + 5⁵ + 7⁷ + 9⁹ + 0⁰ + 8⁸ + 8⁸

= 256 + 27 + 16777216 + 3125 + 823543 + 387420489 + 0 + 16777216 + 16777216 = 438579088

Now you know about properties of Munchausen number. Both the above shown examples are in decimal system. So friends use your grey cells and come up with more such numbers in any base other than decimal.

I know it's little difficult but since so many intelligent people are regular visitors to QuickerMaths.com, I am assured that we will get some answers.

Vineet Patawari