Project Euler/63

Problem Statement

How many n-digit positive integers exist which are also an nth power?

Link: https://projecteuler.net/problem=63

Solution Technique

This one is almost embarrassingly easy...

To check if a number $ a^b $ is $ b $ digits, we can take $ \log_{10}(b) $ and if the value, rounded up, is $ b $, our criteria is met.

For this particular problem, we can stop at $ n=25 $, since ceil(log10(9**25)) = 25

Code

Here is the full solution method - quite simple compared to some of the other Project Euler problems in the 60s range:

	public static void solve() {

		// These are the only numbers that qualify,
		// since 10^n is n+1 digits
		int counter = 0;
		for(int i=1; i<10; i++) { 

			for(int j=1; j<25; j++) { 
				int ndigits = (int)(Math.ceil(j*Math.log10(i)));
				boolean jDigits = (ndigits==j);
				if(jDigits) { 
					counter++;
				}
					
			}
		}
		// This doesn't count 0^1, which is 0, also 1 digit.
		counter++;

		System.out.println(counter);

	}

Link: https://git.charlesreid1.com/cs/euler/src/master/scratch/Round2_050-070/063/Problem063.java