[VA] Short & Sweet Math Challenges #23: "May the 4th Be With You !" Special

[Jeff O.]

(05-10-2018 09:55 PM)Valentin Albillo Wrote:        
Hi, all:

Time to wrap up this S&SMC#23. ...

"We'll call "Selfie" to any positive N-digit integer number which has the property that if you sum its N digits raised to the Nth power you get the original number backwards. For instance, the 7-digit number 5271471 is a Selfie:

      5271471 => 5^7 + 2^7 + 7^7 + 1^7 + 4^7 + 7^7 + 1^7 = 1741725, which is 5271471 backwards

Write a program to find all Selfies from 1 to 9 digits long (for 10-digit HP calcs, 29 in all) or from 1 to 11 digits long (for 12-digit HP calcs, 37 in all). 0 is not a positive number so it's not a Selfie."

Same here, no one posted any code or comments for this one either so I'll also save my original solution for a future article or something. As I said at the beginning of this post, it's a real pity as this Step was solvable (partially or in full) using most any HP calc model...

I'll confess to not having read through your challenge closely enough to see your note that this particular step might be potentially solvable by other models. I think the 71B is a wonderful machine and am glad to have an example, but have never attempted to master its use, so I assumed this challenge was not for me. Upon further review, Step the 6th is the kind of number manipulation challenge that I have enjoyed attempting on various models, along the lines of some of the HHC programming contests. With that said, reading that Egan put 3 hours and one sleepless night into it, and it will continue to haunt him, kind of scares me off a bit. My usual inclination with such problems is to just go ahead and try for a brute force method, then try to optimize. The DM42 is fast, I would like to see how many digits it could handle in a reasonable time by brute force, so if I get the time I may have a go at it.

In any case, thanks for your challenges, please don’t be put off by a lower than hoped-for response. Next time I’ll be sure to read through more carefully!