Question

小学数学问题

将0～9这十个数字分别填入下面算式的□内，每个数字只能用一次；那么满足条件的正确填法共有多少种？
□＋□□＋□□□＝□□□□

Answer 1

由题意可知：
g
e f
+ 9 c d
--------------
1 0 a b
设所有加数数字和为:A=9+c+d+e+f+g,
和的数字和为:B=1+0+a+b
有:A+B=45，A-B=9n.
因为A+B与A-B同奇偶，所以A-B不可能等于偶数，可以是9,或者27。
当A-B=9时，根据和差公式得: A=27，B=18，则a+b=17，只能是9+8，9已使用，不行。
当A-B=27时，根据和差公式得: A=36，B=9，则a+b=8，可以成立
所以，a,b可能为(2, 6) (3, 5) (6, 2) (5, 3)四种。
当(a, b)=(2, 6)，则有e+c=11=3+8=4+7;
当(a, b)=(3, 5)，则有e+c=12=4+8;
当(a, b)=(6, 2)，则有e+c=15=7+8
当(a, b)=(5, 3)，则有e+c=14=6+8;
共有5类，可以使等式成立.
上面5类成立的式子中, 每一类中e与c都可以交换，g、f、d可以交换排列
所以每一类有：(2×1)×(3×2×1)=12 种。
因此满足条件的正确填法共有：5×12=60 (种)

Answer 2

8 + 34 + 579 = 0621

4 + 38 + 579 = 0621

8 + 74 + 539 = 0621

4 + 78 + 539 = 0621

9 + 34 + 578 = 0621

4 + 39 + 578 = 0621

4 + 79 + 538 = 0621

9 + 74 + 538 = 0621

8 + 39 + 574 = 0621

9 + 38 + 574 = 0621

8 + 79 + 534 = 0621

9 + 78 + 534 = 0621

8 + 27 + 496 = 0531

7 + 28 + 496 = 0531

8 + 97 + 426 = 0531

7 + 98 + 426 = 0531

7 + 26 + 498 = 0531

6 + 27 + 498 = 0531

7 + 96 + 428 = 0531

6 + 97 + 428 = 0531

8 + 26 + 497 = 0531

6 + 28 + 497 = 0531

8 + 96 + 427 = 0531

6 + 98 + 427 = 0531

7 + 48 + 296 = 0351

8 + 47 + 296 = 0351

7 + 98 + 246 = 0351

8 + 97 + 246 = 0351

8 + 74 + 269 = 0351

4 + 78 + 269 = 0351

4 + 68 + 279 = 0351

8 + 64 + 279 = 0351

8 + 46 + 297 = 0351

6 + 48 + 297 = 0351

8 + 96 + 247 = 0351

6 + 98 + 247 = 0351

9 + 78 + 264 = 0351

8 + 79 + 264 = 0351

8 + 69 + 274 = 0351

9 + 68 + 274 = 0351

9 + 74 + 268 = 0351

4 + 79 + 268 = 0351

7 + 46 + 298 = 0351

6 + 47 + 298 = 0351

4 + 69 + 278 = 0351

9 + 64 + 278 = 0351

7 + 96 + 248 = 0351

6 + 97 + 248 = 0351

5 + 84 + 973 = 1062

4 + 85 + 973 = 1062

5 + 74 + 983 = 1062

4 + 75 + 983 = 1062

3 + 85 + 974 = 1062

5 + 83 + 974 = 1062

3 + 75 + 984 = 1062

5 + 73 + 984 = 1062

3 + 84 + 975 = 1062

4 + 83 + 975 = 1062

3 + 74 + 985 = 1062

4 + 73 + 985 = 1062

8 + 29 + 476 = 0513

9 + 28 + 476 = 0513

9 + 78 + 426 = 0513

8 + 79 + 426 = 0513

9 + 26 + 478 = 0513

6 + 29 + 478 = 0513

9 + 76 + 428 = 0513

6 + 79 + 428 = 0513

8 + 76 + 429 = 0513

6 + 78 + 429 = 0513

8 + 26 + 479 = 0513

6 + 28 + 479 = 0513

9 + 78 + 156 = 0243

8 + 79 + 156 = 0243

8 + 59 + 176 = 0243

9 + 58 + 176 = 0243

8 + 56 + 179 = 0243

6 + 58 + 179 = 0243

8 + 76 + 159 = 0243

6 + 78 + 159 = 0243

9 + 56 + 178 = 0243

6 + 59 + 178 = 0243

9 + 76 + 158 = 0243

6 + 79 + 158 = 0243

2 + 64 + 987 = 1053

4 + 62 + 987 = 1053

2 + 84 + 967 = 1053

4 + 82 + 967 = 1053

4 + 87 + 962 = 1053

7 + 84 + 962 = 1053

4 + 67 + 982 = 1053

7 + 64 + 982 = 1053

2 + 87 + 964 = 1053

7 + 82 + 964 = 1053

2 + 67 + 984 = 1053

7 + 62 + 984 = 1053

8 + 59 + 167 = 0234

9 + 58 + 167 = 0234

9 + 68 + 157 = 0234

8 + 69 + 157 = 0234

7 + 59 + 168 = 0234

9 + 57 + 168 = 0234

7 + 69 + 158 = 0234

9 + 67 + 158 = 0234

7 + 58 + 169 = 0234

8 + 57 + 169 = 0234

7 + 68 + 159 = 0234

8 + 67 + 159 = 0234

2 + 46 + 987 = 1035

6 + 42 + 987 = 1035

2 + 86 + 947 = 1035

6 + 82 + 947 = 1035

2 + 47 + 986 = 1035

7 + 42 + 986 = 1035

2 + 87 + 946 = 1035

7 + 82 + 946 = 1035

6 + 47 + 982 = 1035

7 + 46 + 982 = 1035

6 + 87 + 942 = 1035

7 + 86 + 942 = 1035

4 + 35 + 987 = 1026

5 + 34 + 987 = 1026

4 + 85 + 937 = 1026

5 + 84 + 937 = 1026

5 + 43 + 978 = 1026

3 + 45 + 978 = 1026

5 + 73 + 948 = 1026

3 + 75 + 948 = 1026

8 + 45 + 973 = 1026

5 + 48 + 973 = 1026

8 + 75 + 943 = 1026

5 + 78 + 943 = 1026

5 + 37 + 984 = 1026

7 + 35 + 984 = 1026

5 + 87 + 934 = 1026

7 + 85 + 934 = 1026

8 + 43 + 975 = 1026

3 + 48 + 975 = 1026

4 + 37 + 985 = 1026

7 + 34 + 985 = 1026

4 + 87 + 935 = 1026

7 + 84 + 935 = 1026

8 + 73 + 945 = 1026

3 + 78 + 945 = 1026

2 + 53 + 791 = 0846

3 + 52 + 791 = 0846

2 + 93 + 751 = 0846

3 + 92 + 751 = 0846

1 + 53 + 792 = 0846

3 + 51 + 792 = 0846

3 + 91 + 752 = 0846

1 + 93 + 752 = 0846

2 + 51 + 793 = 0846

1 + 52 + 793 = 0846

2 + 91 + 753 = 0846

1 + 92 + 753 = 0846

2 + 83 + 491 = 0576

3 + 82 + 491 = 0576

2 + 93 + 481 = 0576

3 + 92 + 481 = 0576

1 + 83 + 492 = 0576

3 + 81 + 492 = 0576

3 + 91 + 482 = 0576

1 + 93 + 482 = 0576

2 + 81 + 493 = 0576

1 + 82 + 493 = 0576

2 + 91 + 483 = 0576

1 + 92 + 483 = 0576

2 + 45 + 691 = 0738

5 + 42 + 691 = 0738

2 + 95 + 641 = 0738

5 + 92 + 641 = 0738

5 + 41 + 692 = 0738

1 + 45 + 692 = 0738

5 + 91 + 642 = 0738

1 + 95 + 642 = 0738

2 + 41 + 695 = 0738

1 + 42 + 695 = 0738

2 + 91 + 645 = 0738

1 + 92 + 645 = 0738

2 + 75 + 391 = 0468

5 + 72 + 391 = 0468

2 + 95 + 371 = 0468

5 + 92 + 371 = 0468

5 + 71 + 392 = 0468

1 + 75 + 392 = 0468

5 + 91 + 372 = 0468

1 + 95 + 372 = 0468

2 + 71 + 395 = 0468

1 + 72 + 395 = 0468

2 + 91 + 375 = 0468

1 + 92 + 375 = 0468

3 + 54 + 762 = 0819

4 + 53 + 762 = 0819

4 + 63 + 752 = 0819

3 + 64 + 752 = 0819

2 + 54 + 763 = 0819

4 + 52 + 763 = 0819

2 + 64 + 753 = 0819

4 + 62 + 753 = 0819

2 + 53 + 764 = 0819

3 + 52 + 764 = 0819

2 + 63 + 754 = 0819

3 + 62 + 754 = 0819

5 + 43 + 681 = 0729

3 + 45 + 681 = 0729

5 + 83 + 641 = 0729

3 + 85 + 641 = 0729

1 + 45 + 683 = 0729

5 + 41 + 683 = 0729

1 + 85 + 643 = 0729

5 + 81 + 643 = 0729

1 + 43 + 685 = 0729

3 + 41 + 685 = 0729

1 + 83 + 645 = 0729

3 + 81 + 645 = 0729

2 + 71 + 386 = 0459

1 + 72 + 386 = 0459

2 + 81 + 376 = 0459

1 + 82 + 376 = 0459

2 + 76 + 381 = 0459

6 + 72 + 381 = 0459

2 + 86 + 371 = 0459

6 + 82 + 371 = 0459

1 + 76 + 382 = 0459

6 + 71 + 382 = 0459

1 + 86 + 372 = 0459

6 + 81 + 372 = 0459

Answer 3

因为 要使最后的和为四位数

所以 显然三位数的开头必为9

且一位数加上两位数不可能大于200

又因题目要求数字不重复

所以 显然四位数的开头必为1 0

理论分析我也只能分析到这里了。。。。。 抱歉啊

我也只算出了一种填法，其他种的真的应该找不到了

5 + 34 + 987 = 1026

希望对你有所帮助

Answer 4

注：每位数字开头不能为零！
5 + 84 + 973 = 1062
4 + 85 + 973 = 1062
5 + 74 + 983 = 1062
4 + 75 + 983 = 1062
3 + 85 + 974 = 1062
5 + 83 + 974 = 1062
3 + 75 + 984 = 1062
3 + 84 + 975 = 1062
5 + 73 + 984 = 1062
4 + 73 + 985 = 1062
3 + 74 + 985 = 1062
4 + 83 + 975 = 1062
2 + 64 + 987 = 1053
4 + 62 + 987 = 1053
2 + 84 + 967 = 1053
7 + 84 + 962 = 1053
4 + 82 + 967 = 1053
4 + 87 + 962 = 1053
7 + 64 + 982 = 1053
4 + 67 + 982 = 1053
2 + 67 + 984 = 1053
7 + 82 + 964 = 1053
2 + 87 + 964 = 1053
7 + 62 + 984 = 1053
2 + 46 + 987 = 1035
6 + 42 + 987 = 1035
2 + 86 + 947 = 1035
6 + 82 + 947 = 1035
2 + 47 + 986 = 1035
2 + 87 + 946 = 1035
6 + 47 + 982 = 1035
7 + 82 + 946 = 1035
6 + 87 + 942 = 1035
7 + 86 + 942 = 1035
7 + 46 + 982 = 1035
7 + 42 + 986 = 1035
4 + 35 + 987 = 1026
5 + 43 + 978 = 1026
5 + 34 + 987 = 1026
4 + 85 + 937 = 1026
5 + 84 + 937 = 1026
3 + 45 + 978 = 1026
5 + 73 + 948 = 1026
8 + 75 + 943 = 1026
3 + 75 + 948 = 1026
8 + 45 + 973 = 1026
5 + 48 + 973 = 1026
5 + 37 + 984 = 1026
8 + 73 + 945 = 1026
7 + 35 + 984 = 1026
5 + 78 + 943 = 1026
5 + 87 + 934 = 1026
7 + 85 + 934 = 1026
8 + 43 + 975 = 1026
4 + 37 + 985 = 1026
3 + 48 + 975 = 1026
7 + 34 + 985 = 1026
3 + 78 + 945 = 1026
4 + 87 + 935 = 1026
7 + 84 + 935 = 1026
怎么样？

Answer 5

60种

Answer 6

5+73+948=1026