小學三年級數學題！用數字 1 到 8 組成兩個三位數使其和為 1000

用數字 1 到 8 組成兩個三位數使其和為 1000，這兩個三位數里面的數字不能重復。

問能寫幾組？

用小學三年級的解題思路還真沒想到。

只好用笨方法跑個小程序了。

L=list(range(1,9))
#print(L)

s=""
S=[]
for l in L:
    for l1 in L:
        for l2 in L:
            if str(l)<>str(l1) and str(l)<>str(l2) and str(l1)<>str(l2):
                s=str(l) + str(l1) + str(l2)
                S.append(s)


def IsSame(a,b):
    v=True
    for al in a:
        for bl in b:
            if al==bl:
                v= False
    return v


C1000=[]
for c in S:
    v=1000-int(c)
    if str(v)[0]<>str(v)[1] and str(v)[0]<>str(v)[2] and str(v)[1]<>str(v)[2] and str(v)[2]<>'9' and IsSame(c,str(v)):
        C1000.append(c)

#print(C1000)
#print(len(C1000))

n=1
DisplayList=[]
for i in range(len(C1000)/2):
    DisplayList.append(C1000[i] + " + " + C1000[len(C1000)-n] + " = 1000")
    n+=1

print(DisplayList)

最終結果有 24 組：

'124 + 876 = 1000', '126 + 874 = 1000', 
'143 + 857 = 1000', '147 + 853 = 1000', 
'153 + 847 = 1000', '157 + 843 = 1000', 
'174 + 826 = 1000', '176 + 824 = 1000', 
'214 + 786 = 1000', '216 + 784 = 1000', 
'284 + 716 = 1000', '286 + 714 = 1000',
'342 + 658 = 1000', '348 + 652 = 1000', 
'352 + 648 = 1000', '358 + 642 = 1000', 
'413 + 587 = 1000', '417 + 583 = 1000',
'432 + 568 = 1000', '438 + 562 = 1000', 
'462 + 538 = 1000', '468 + 532 = 1000', 
'483 + 517 = 1000', '487 + 513 = 1000'