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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?

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  • $\begingroup$ 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? $\endgroup$
    – Rosie F
    Sep 29 at 7:13
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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.

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    $\begingroup$ Could you note by what method you arrived at this answer? Trial and error? $\endgroup$
    – bobble
    Sep 26 at 22:23

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