SOLUTION: How many whole numbers are there, whose squares and cubes have the same number of digits?

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Question 1126191: How many whole numbers are there, whose squares and cubes have the same number of digits?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Depends on what you mean by "whole number". Some mathematicians say a whole number is a non-negative integer, some say it is just an integer.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52788) (Show Source):
You can put this solution on YOUR website!
.

It is clear even without my explanations that for n >= 10 the cube of n, , has MORE digits than the square . Therefore, only 1-digit numbers must be checked n n^2 n^3 ----------------- 0 0 0 (*) 1 1 1 (*) 2 4 8 (*) 3 9 27 4 16 64 (*) 5 25 125 6 36 256 7 49 8 9 ---------------- For your convenience, I marked the favorable numbers by (*), so you can calculate the ANSWER on your own.