Think of a number

Posted By:
Lord Lucan
in somewhere strange Nov 25, 2004

The Times has a story about a man who does amazing calculations:
Q. What is the 13th root of 70664373816742861
02234008830240157375704233170702632731
26972151600039570906541997314191454938
9684111?
A. 47,941,071
Is there less to this than it seems? What we aren't told is what the solver was expected to do, was he expecting to be given any number and asked for any root or was he expecting a 100digit number and expecting to be asked to find the 13th root?
The latter, while being difficult is a lot easier. There are only about eight million whole numbers that are the 13th root of 100 digit numbers and we are told elsewhere in the story that the solver has prodigious memory skills  has he got a mnemonic for finding the answer?
Roger Boyes (the author of the piece) doesn't seem to know much about maths  he thinks that a scientific calculator can be used to solve this problem  one with 100 digits that is (it'd be as wide as my desk). Also he suggests that a 100 digit number chosen at random has an integer 13th root  when in fact most don't (most of the roots would be irrational and therefore incalculable).

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