Four-Digit Perfect Powers Puzzle: Find the Number That Is a Square, Cube, and Fourth Power

A Step Up in Difficulty: The Perfect Powers Puzzle

Alright, alright — that last one was too easy. Time to raise the stakes.

A certain four-digit number is a perfect square. If you remove the first digit from the left, the remaining number is a perfect cube. If you remove the first two digits, the remaining number is a fourth power of an integer. Find this number.

How to Approach This Perfect Powers Problem

The puzzle sits at a beautiful intersection of number theory and logical elimination. You don’t need advanced mathematics — just a solid understanding of perfect powers and a methodical approach.

Start from the smallest piece of information: what two-digit numbers are fourth powers of integers? That’s a short list. Then work your way up through three-digit perfect cubes that end with those digits, and finally check which four-digit perfect squares contain one of those cubes as a suffix.

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