This post is going to be a pretty short one. Now that I have tasted blood again, I managed to “solve” another Project Euler problem just before hitting the hay last night. I’m still working on the supposed to be easy ones though.
I put “solved” in quotation marks due to the massive sledgehammer which I used for arriving at the solution…a simple for-loop. Does 1 satisfy the given definition? What about 2? And 3? Bang! Bang! Bang!
Using a dumb loop was the first thought that occurred to me on how I could solve this challenge and I didn’t get any smarter in the end.
I started by consulting Wolfram MathWorld to find out more about this numerical phenomenon. Just to discover Narcissistic Numbers. Which is NOT the solution to this given problem.
An n-digit number that is the sum of the nth powers of its digits is called an n-narcissistic number.
Below this definition MathWorld displays a nice little table of all the numbers that satisfy this definition up to n equals 39.
That was easy. For n equals 5 the numbers I was looking for are 54748, 92727, 93084.
These are not the numbers you’re looking for.
Obi -Wan Kenobi
Or to be a bit more precise, these are not the only numbers required to reach the target sum.
After several failed attempts to submit 240559 (54748 + 92727 + 93084) I came to the conclusion that most likely I am not smarter than Project Euler and started thinking about what I was missing here.
If you read the problem description carefully, it becomes clear that your search is not limited to n-narcissistic numbers only. For example 4150 is just fine as well:
4150: 45 + 15 + 55 + 05 = 4150.
The number doesn’t have to be precisely n-digits long. I hope this helps.
Now I have to read the forum posts as usual. And then move on to the next problem on my list, Coin sums.