Determine the respective last digit and the first digit (reading left to right) in the base ten expansion of


23²³²³²³

Remember that this is evaluated starting at the top-right and proceeding down and to the left.

(In reply to computer-aided solution to part 1 by Charlie)

23^(23^23) itself is a 28433514504467493128360275814989-digit number.  So even if we took log(23) and multiplied by this huge number (presumably by taking log(log(23)) and adding log(23^(23^23)) ), we'd still be in trouble taking antilog (raising 10 to the power) twice.  If we only had to do it once, we could get the first few digits by truncating the integer part. But since the result has to be used again to take the antilog again, we can't truncate that integer part of the original logarithm.

Posted by Charlie on 2013-11-15 12:24:35