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Problem 62¶

Cubic Permutations¶

The cube, $41063625$ ($345^3$), can be permuted to produce two other cubes: $56623104$ ($384^3$) and $66430125$ ($405^3$). In fact, $41063625$ is the smallest cube which has exactly three permutations of its digits which are also cube.

Find the smallest cube for which exactly five permutations of its digits are cube.

立方数置換¶

立方数 $41063625$ ($345^3$) は, 桁の順番を入れ替えると2つの立方数になる: $56623104$ ($384^3$) と $66430125$ ($405^3$) である. $41063625$は, 立方数になるような桁の置換をちょうど3つもつ最小の立方数である.

立方数になるような桁の置換をちょうど5つもつ最小の立方数を求めよ.