Number Curiosities

The number 17772 has a property that makes it unique among five-digit numbers: it is the sum of the squares of the five two-digit numbers formed when you read its digits left to right (and cycle back at the end). That is, 

17772= 17x17 + 77x77 + 77x77 + 72x72 + 21x21

Although no other five-digit number has this property, it’s also true that there is a unique five-digit number equal to the sum of the two-digit numbers formed by its own digits reading from RIGHT to LEFT. In other words, there is a unique solution to this “ cryptarithm “ (but note that repeated digits are allowed, so different letters can represent the same digit):

ABCDE = BAxBA + AExAE + EDxED + DCxDC + CBxCB

I found the solutions to both these original problems by using a spreadsheet, and the second one particularly surprised me. Perhaps it will surprise you too.

As I mentioned a couple of posts back, my story ”The Hyland Resolution” in the anthology PLANETARY ANTHOLOGY: LUNA, has a main character who likes number puzzles, and this becomes important in an unexpected way. I hope you’ll pick up the book and enjoy my story as well as all the others!