Math Whiz Breaks Calculation Record

Two questions that weren't answered in the article:

1. How many digits of precision were required in the answer?

2. Was this an open ended question, as in the nth root of an x digit number, or did he know he would have to find the 13th root of a 20 digit number beforehand?

This is not a difficult problem for anyone with a math, science or engineering background. If all you need is 2 or 3 digits of precision, I'd expect any working scientist or similar to be able to do this in their head within a minute. In fact, if he knew he was going to be asked to take the 13th root of a 20 digit number and only needed two or three digits, I'd wonder why it took him so long. To make this notable, my guess is that he only knew that the question would be of the form "Find the nth root of an x digit number", and that he needed several digits of precision (like a half dozen).

But then most of us (me included) don't have a freakin' clue what any of this means, consequently it sounds damn impressive.

OK, the concept is straight forward if you know a little about logs or scientific notation. The 20 digit number can be written as X * 10^20 (X is the mantissa, or precision part, and would range from 1 to just less than 10). You want to find a value that is the 13th root of this, or Y^13 = X * 10^20. This value can be written in scientific notation also, Z * 10^A. So, your exponent is just 20/13, or a little over 1.5. In other words, a little more than 10 times the square root of 10, or around 35. The mantissa is the 13th root of X. As X only ranges from 1 to 10, that's not a very big number, nor does it have a large range (like less than 1.2). Thus, you see very quickly (and in your head) that the 13th root of any 20 digit number must range from the mid 30's to the low 40's. Now, some folks have memorized their times tables to more than 100x100, and for someone like that, this is not a mind bending problem.

Jim, you took all the mystery out of it :)

Not a bad record to have anyhow.