Person in Charge

• 035966_L3

Problem Description

A cube number $x$ is called a "distinctive digit cube" if all its decimal digits are different.

Examples:

• $343$ is NOT a "distinctive digit cube" (repeated $3$'s).
• $841$ is NOT a "distinctive digit cube" (not a perfect cube).
• $512$ is a "distinctive digit cube".

Obviously, a "distinctive digit cube" $x$ cannot have more than $10$ digits.

Find all "distinctive digit cubes" with $1$ to $10$ digits respectively. Note that $0$ is considered a valid 1-digit "distinctive digit cube".

Answer Format

This is an output-only problem.

You must submit a zip file named cube.zip containing $\bm{10}$ text files:

• 1.txt (1-digit cubes)
• 2.txt (2-digit cubes)
• ...
• 10.txt (10-digit cubes)

Requirements:

• One number per line.
• Numbers in ascending order.
• Only "distinctive digit cubes".
• No empty lines.
• No additional characters.

Example: (4.txt)

1728
2197
4096
****
....