ABCD×4=DCBA 求:A,B,C,

1个回答

  • 由题意得:

    4A=D

    A 为1或者2

    假定A = 1,D = 4,但 4*D 的个位不是1,所只能取 A = 2.4*D 的个位是 2 D = 8成立

    (2000 + 100B + 10C + 8)*4 = 8000 + 100C + 10B + 2

    400B + 40C + 32 = 100C + 10B + 2

    40B + 4C + 3 = 10C + B

    39B = 6C - 3 = 3(2C - 1)

    13B = 2C - 1 .能被13整除,所以:

    B = 1 .C = 7

    原式为:2178*4 = 8712