The torn number label that rebuilds itself by squaring
A label reading 3025 tears in half into "30" and "25." Add the two halves together (30 + 25 = 55) and square that sum (55 × 55), and you get back the complete original number, 3025. Henry Dudeney's puzzle: find another four-digit number, with all four digits different, that can be split exactly in half down the middle and does the very same trick.
Reveal the answer
9801. Split it into 98 and 01, add them (98 + 1 = 99), and square: 99 × 99 = 9,801. (2025 works by the same trick — 20+25=45, 45²=2025 — but it's ruled out by the no-repeated-digits condition.) From Henry Dudeney's Amusements in Mathematics (1917), puzzle No. 113, "The Torn Number."
— Henry Dudeney, Amusements in Mathematics — Puzzle No. 113, "The Torn Number," 1917