Enigma 1628: Power crazy
13 December 2011
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From New Scientist #2794, 8th January 2011 [link]
My godson is 5 years old. When you work out his age raised to a power equal to itself you get 55 = 3125, which ends with his age.
Similarly, if you take my age in years and raise it to a power equal to itself then the answer ends with my age. And if you reverse the two different digits of my age and work out my “reverse age” raised to a power equal to itself then the answer ends with my reverse age.
I was also surprised to find that, if you raise my reverse age to a power equal to my age then the answer also ends with my reverse age.
Clearly I do not expect you to work out any of these powers, as they all consist of over 100 digits! However, you should still be able to answer the question: how old am I?