Question

我将进行数学竞赛,使写作方案能够解决问题。

该法典试图解决这一问题:

WHITE+WATER=PICNIC 每一封不同的字母代表数。计算由事先知情同意委员会代表的人数。

No imports are allowed (tqdm was just a progress bar). What I tried is below. At the rate of which my computer goes, it is not fast enough for the times competition because it needs to range over 10 to the power of digits there is.

这一问题是否有明确的解决办法?

from tqdm import tqdm

def find_solution():
    for W in tqdm(range(10)):
        for H in tqdm(range(10), desc= H ):
            for I in tqdm(range(10), desc= I ):
                for T in tqdm(range(10)):
                    for E in tqdm(range(10)):
                        for A in (range(10)):
                            for R in (range(10)):
                                for P in (range(1, 10)): # P cannot be 0
                                    for C in (range(10)):
                                        for N in (range(10)):
                                            white = W * 10000 + H * 1000 + I * 100 + T * 10 + E
                                            water = W * 10000 + A * 1000 + T * 100 + E * 10 + R
                                            picnic = P * 100000 + I * 10000 + C * 1000 + N * 100 + I * 10 + C

                                            if white + water == picnic:
                                                return { W : W,  H : H,  I : I,  T : T,  E : E,  A : A,  R : R,  P : P,  C : C,  N : N}

    return None

solution = find_solution()

if solution:
    print("Solution found:")
    print(solution)
else:
    print("No solution found.")

Answer 1

意见:

P=1 due to a carry to its sixth digit
W must be 5-9 due to a carry being generated (1)
No letter can be the same value as another letter.

def find_solution():
    P = 1
    for W in range(5,10):
        for H in range(10):
            if H in (P,W): continue
            for I in range(10):
                if I in (H,P,W): continue
                for T in range(10):
                    if T in (I,H,P,W): continue
                    for E in range(10):
                        if E in (T,I,H,P,W): continue
                        for A in range(10):
                            if A in (E,T,I,H,P,W): continue
                            for R in range(10):
                                if R in (A,E,T,I,H,P,W): continue
                                for C in range(10):
                                    if C in (R,A,E,T,I,H,P,W): continue
                                    for N in range(10):
                                        if N in (C,R,A,E,T,I,H,P,W): continue
                                        white = W * 10000 + H * 1000 + I * 100 + T * 10 + E
                                        water = W * 10000 + A * 1000 + T * 100 + E * 10 + R
                                        picnic = P * 100000 + I * 10000 + C * 1000 + N * 100 + I * 10 + C

                                        if white + water == picnic:
                                            print(f  WHITE= {white} )
                                            print(f  WATER= {water} )
                                            print(f PICNIC={picnic} )
                                            print()

find_solution()

产出(2项解决办法,约1项):

 WHITE= 83642
 WATER= 85427
PICNIC=169069

 WHITE= 85642
 WATER= 83427
PICNIC=169069

当然,如果你能够使用图书馆(约0.3秒)。 Note the documentation of itertools.permutations 只执行粗 Python的甲草胺,但低于上文硬编码版本:

from itertools import permutations

def find_solution():
    P=1
    for W,H,I,T,E,A,R,C,N in permutations([0,2,3,4,5,6,7,8,9]):
        if W < 5: continue
        white = W * 10000 + H * 1000 + I * 100 + T * 10 + E
        water = W * 10000 + A * 1000 + T * 100 + E * 10 + R
        picnic = P * 100000 + I * 10000 + C * 1000 + N * 100 + I * 10 + C

        if white + water == picnic:
            print(f  WHITE= {white} )
            print(f  WATER= {water} )
            print(f PICNIC={picnic} )
            print()

find_solution()

Answer 2

I ve除去了 t木进口品,用固定范围 lo替代了nes树脂。这应当使法典更加简单、快捷,而不使用外部进口。

def find_solution():
    for W in range(10):
        for H in range(10):
            for I in range(10):
                for T in range(10):
                    for E in range(10):
                        for A in range(10):
                            for R in range(10):
                                for P in range(1, 10):  # P cannot be 0
                                    for C in range(10):
                                        for N in range(10):
                                            white = W * 10000 + H * 1000 + I * 100 + T * 10 + E
                                            water = W * 10000 + A * 1000 + T * 100 + E * 10 + R
                                            picnic = P * 100000 + I * 10000 + C * 1000 + N * 100 + I * 10 + C

                                            if white + water == picnic:
                                                return { W : W,  H : H,  I : I,  T : T,  E : E,  A : A,  R : R,  P : P,  C : C,  N : N}

    return None

solution = find_solution()

if solution:
    print("Solution found:")
    print(solution)
else:
    print("No solution found.")

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