Edit post

Title

### 題目
![](http://topick.hket.com/res/v3/image/content/1390000/1392035/math3_1024.jpg)

### Rules
1. `A`, `C`, `E`, `G` != 0
2. 所有數字既range係[0, 9] 
3. 數字冇重覆

### Code
    #!/usr/bin/env pypy3
    from itertools import permutations

def check(i):
        if i[0] == 0 or i[2] == 0 or i[4] == 0 or i[6] == 0:
            return
        ab = i[0] * 10 + i[1]
        cd = i[2] * 10 + i[3]
        ef = i[4] * 10 + i[5]
        if ab - cd != ef:
            return
        gh = i[6] * 10 + i[7]
        ppp = i[8] * 100 + i[8] * 10 + i[8]
        if ef + gh == ppp:
            print("{0} - {1} = {2}, {2} + {3} = {4}".format(ab, cd, ef, gh, ppp))

if __name__ == '__main__':
        for i in permutations(range(0, 10), 9):
            check(i)

### 如果已知ppp = 111
    #!/usr/bin/env pypy3
    from itertools import permutations

def check(i):
        if i[0] == 0 or i[2] == 0 or i[4] == 0 or i[6] == 0:
            return
        ab = i[0] * 10 + i[1]
        cd = i[2] * 10 + i[3]
        ef = i[4] * 10 + i[5]
        if ab - cd != ef:
            return
        gh = i[6] * 10 + i[7]
        ppp = 111
        if ef + gh == ppp:
            print("{0} - {1} = {2}, {2} + {3} = {4}".format(ab, cd, ef, gh, ppp))

if __name__ == '__main__':
        for i in permutations(list(range(2, 10)) + [0], 9):
            check(i)
答案

85 - 46 = 39, 39 + 72 = 111
    86 - 54 = 32, 32 + 79 = 111
    90 - 27 = 63, 63 + 48 = 111
    90 - 63 = 27, 27 + 84 = 111
    95 - 27 = 68, 68 + 43 = 111
    pypy3 ./primary-math.py  0.10s user 0.02s system 98% cpu 0.123 total

### 結論
出題果個正一戇鳩。
___
### 高效率版本
用左加強版解法既algorithm解一解原題目。唔知點解`python3`快過`pypy3`。

#!/usr/bin/env python3
    from itertools import permutations

PPP = 111

def check_last_4(i):
        if i[0] == 0 or i[2] == 0:
            return 0
        EF, GH = i[0] * 10 + i[1], i[2] * 10 + i[3]
        if EF + GH == PPP:
            return EF
        return 0

def check_first_4(i, EF):
        if i[0] == 0 or i[2] == 0:
            return 0
        AB, CD = i[0] * 10 + i[1], i[2] * 10 + i[3]
        if AB - CD == EF:
            return 1

if __name__ == '__main__':
        for i in permutations(set(range(10)) - {1}, 4):
            EF = check_last_4(i)
            if EF == 0:
                continue
            for j in permutations(set(range(10)) - set(i) - {1}, 4):
                if check_first_4(j, EF):
                    print(j, i)

### 結果
    (9, 0, 6, 3) (2, 7, 8, 4)
    (8, 6, 5, 4) (3, 2, 7, 9)
    (8, 5, 4, 6) (3, 9, 7, 2)
    (9, 0, 2, 7) (6, 3, 4, 8)
    (9, 5, 2, 7) (6, 8, 4, 3)
    python ./eff.py  0.05s user 0.00s system 98% cpu 0.055 total

Content

Password

Edit post

Preview

Powered by Simple Blog