The Mudcat Café TM
Thread #152040   Message #3556065
Posted By: DMcG
04-Sep-13 - 10:55 AM
Thread Name: BS: Who else plays little # games?
Subject: RE: BS: Who else plays little # games?
Yes, it was I. My phone doesn't like holding cookies so I often forget to check whether it still remembers who I am.


Going back to the original question: I haven't spent the ten minutes investigating this because it is a much harder problem than it first appears. The difficulty is that it is a mixture of a properties about numbers and properties about notation. In particular when you get a carry' it becomes really difficult to express 'the sum of the digits'.    On the other hand, the 81 is part of a more obsure set that is quite interesting: suppose you write a number in base N rather than base 10. Then, for every N there is a number that has the same property of the sum of the digits matching the square root.   So for example 41 in base 6 is 25 in base ten, which is the square of 4+1.

This doesn't need more than school algebra to work out what the number is, but even so it might take a few minutes. The Eureka! Moment when you see how to solve it might make the exercise worth it.