FOUR是四位数 SEVEN十五位数
F 的值可以由 SEVEN 的范围求得
F 的值与 SEVEN的范围的关系如下
F 5 6 7 8 9
SEVEN 10000~10500~12250~14000~15750~17500
S = 1 可以确定
E,V,N 有如下关系:
10000 + 1000E + 100V + 10E + N ≡ 0 (mod 7)
即:
2(E + V) + N ≡ 3 (mod 7)
N,R 有如下关系:4N ≡ 7R (mod 10)
他们的值对应如下:
N 0 1 2 3 4 5 6 7 8 9
R 0 2 4 6 8 0 2 4 6 8
N = 0, R = 0 → N = R 不可
N = 1, R = 2 → N = S不可
N = 2, R = 4 → E + V ≡ 4 (mod 7)
7904/13832, 8944/15652, 9464/16562
N = 3, R = 6 → E + V ≡ 0 (mod 7)
7156/12523, 8716/15253, 9756/17073, 9116/15953
N = 4, R = 8 → E + V ≡ 3 (mod 7)
5888/10304, 7448/13034, 7848/13734
N = 5, R = 0 → E + V ≡ 6 (mod 7)
7100/12425, 8140/14245, 8540/14945, 9580/16765
N = 6, R = 2 → E + V ≡ 2 (mod 7)
8312/14546, 8832/15456
N = 7, R = 4 → E + V ≡ 5 (mod 7)
6004/10507, 8604/15057
N = 8, R = 6 → E + V ≡ 1 (mod 7)
7736/13538
N = 9, R = 8 → E + V ≡ 4 (mod 7)
5948/10409
检验一下上面的数,满足条件的只有:
7904/13832
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