Perfect Square
A number times itself — squared away neatly.
The square of an integer, like 144, 1024 or 998001. RNGdle counts 0 too: 0² = 0, fair and square.
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A square's rarity can be read straight off the square root: the range holds exactly 1,001 squares, 0² through 1000², or 0.1%. The gap between consecutive squares is 2k+1 and keeps widening, so squares thin out as numbers grow — only 683 of them are six-digit.
Squares carry an elegant fingerprint: they always have an odd number of divisors. Divisors normally come in pairs (d and n/d), but the square root pairs with itself, leaving one extra. In the classic locker puzzle, the doors left open are exactly the perfect squares.
Trivia: 998001 = 999² is a Kaprekar number — split it into 998 and 001 and the sum comes back to 999. And the numbers that are both square and triangular number only 0, 1, 36, 1225 and 41616 in range, generated by a Pell equation.