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Mathematics Problem

發問:

The number is unique There is just one 2-digit number whose square and cube, between them, use up each of the ten digits 0, 1, 2, 3, ... , 9 only once. Can you find it? explain your methods else

最佳解答:

first, the number should not be ended with 0,1,5,6, because, when a number is ended with 0,1,5,6, its square or cube will have the same end. second, two numbers will share 10digits, thus,square will get 4 and cubic got 6. ie x^2>=1000 and x^3>=100000 x>=31.623 and x>=46.416 Thus x should be larger than 46 2007-02-07 00:17:53 補充： After the processing of excel, the number is 6969^2 = 476169^3 = 328509

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