What is the smallest $9$-digit number that has all the digits from $1$ to $9$ exactly once and is also a perfect square?
Please give me a method that doesn't involve programming.
2026-04-19 05:18:36.1776575916
Smallest pandigital number perfect square
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Just look up A036744, the penholodigital squares.
The possible solutions are
139854276, 152843769, 157326849, 215384976, 245893761, 254817369,
326597184, 361874529, 375468129, 382945761, 385297641, 412739856,
523814769, 529874361, 537219684, 549386721, 587432169, 589324176,
597362481, 615387249, 627953481, 653927184, 672935481, 697435281,
714653289, 735982641, 743816529, 842973156, 847159236, 923187456
With square roots
11826, 12363, 12543, 14676, 15681, 15963,
18072, 19023, 19377, 19569, 19629, 20316,
22887, 23019, 23178, 23439, 24237, 24276,
24441, 24807, 25059, 25572, 25941, 26409,
26733, 27129, 27273, 29034, 29106, 30384