# The digits of the cube of a 3-digit number X

The digits of the cube of a certain 3-digit number X are, from left to right, the square of a 2-digit number, followed by the square of another 2-digit number, followed by one digit. (Everything is base 10.) What number is X?

• This is a cute digit curiosity, but how is it a puzzle? Can anyone find a solution containing an "aha!" insight which enables you to find the answer without brute-forcing the cubes of all 3-digit integers until you find it? Sep 29, 2021 at 7:13

## 1 Answer

The number you're looking for is:

1,442,897

The three digit number $$x$$ is:

113

The two, two digit numbers ($$y$$ and $$z$$) are:

$$y = 12$$ and $$z = 17$$; squared, these are $$144$$ and $$289$$ respectively.

The one digit number is:

7

Concatenating these together gives us:

$$x^3 = 1442897$$

Note: I brute forced my answer since the tag wasn’t specified.

• Could you note by what method you arrived at this answer? Trial and error? Sep 26, 2021 at 22:23