puzzleup 2011

newkid · 发表于 2011-9-8 00:07

第6题和第一题有些相似。

#7: Close and Different

Use all the nine numerals from 1 to 9 once and form four numbers (A, B, C, D) such that divisions A/B and C/D produce different but closest results. (ie. Absolute value of A/B-C/D should be minimum.)

Please enter the four numbers from the smallest to the largest, with commas between them.

Example: If the numbers were 12/789, 6/345, your answer should read 6,12,345,789

利用1-9构成四个数ABCD使得 A/B-C/D 的绝对值最小。

假如用暴力法共有 9! * (1*6+2*5+3*4+4*3+5*2+6*1) = 20321280 次计算，似乎也不是不可能。可以想办法再排除一些对称的排列。

lastwinner · 发表于 2011-9-8 01:26

原帖由 newkid 于 11-8-11 22:37 发表
奥数哥很久不来了，要不然请他指导一下。去年他说要研究哥德巴赫猜想，不知道搞出来没有，报纸上也没见报道。

我承认我笑了

lastwinner · 发表于 2011-9-8 01:31

原帖由 newkid 于 11-9-8 00:07 发表
第6题和第一题有些相似。

#7: Close and Different

Use all the nine numerals from 1 to 9 once and form four numbers (A, B, C, D) such that divisions A/B and C/D produce different but closest results. (ie. Absolute value of A/B-C/D should be minimum.)

Please enter the four numbers from the smallest to the largest, with commas between them.

Example: If the numbers were 12/789, 6/345, your answer should read 6,12,345,789

利用1-9构成四个数ABCD使得 A/B-C/D 的绝对值最小。

假如用暴力法共有 9! * (1*6+2*5+3*4+4*3+5*2+6*1) = 20321280 次计算，似乎也不是不可能。可以想办法再排除一些对称的排列。

A/B和 C/D要尽可能的接近，由于是求最小的绝对值，所以可以假设 A/B一定稍微微微的大于C/D
A/B>C/D => A*D > B*C ，然后呢 A*D和B*C尽可能的接近

newkid · 发表于 2011-9-8 01:54

很不雅的暴力法：
WITH digits AS (
SELECT CAST(REPLACE(SYS_CONNECT_BY_PATH(lv,','),',') AS VARCHAR2(9)) AS str
  FROM (SELECT LEVEL lv FROM DUAL CONNECT BY LEVEL<=9)
WHERE LEVEL=9
CONNECT BY NOCYCLE PRIOR lv<>lv
)
SELECT SUBSTR(str,1,length_A) A
   ,SUBSTR(str,length_A+1,length_AB-length_A) B
   ,SUBSTR(str,length_AB+1,length_C) C
   ,SUBSTR(str,length_AB+length_C+1) D
  FROM ( SELECT *
         FROM digits
            ,(SELECT 2 AS length_AB FROM DUAL UNION ALL SELECT 3 FROM DUAL UNION ALL SELECT 4 FROM DUAL)
            ,(SELECT LEVEL length_A FROM DUAL CONNECT BY LEVEL<=3)
            ,(SELECT LEVEL length_C FROM DUAL CONNECT BY LEVEL<=6)
      WHERE length_A<length_AB AND length_C<9-length_AB
            AND SUBSTR(str,1,length_A)/SUBSTR(str,length_A+1,length_AB-length_A)
               <>SUBSTR(str,length_AB+1,length_C)/SUBSTR(str,length_AB+length_C+1)
      ORDER BY ABS(SUBSTR(str,1,length_A)/SUBSTR(str,length_A+1,length_AB-length_A)
               -SUBSTR(str,length_AB+1,length_C)/SUBSTR(str,length_AB+length_C+1)
               )
      )
WHERE ROWNUM=1
;

A       B       C    D
--------  --------- ------ ---------
1       826    9    7435

Elapsed: 00:01:09.20

由于对称的关系可以假设AB的长度小于CD的长度，砍掉一半。

solomon_007 · 发表于 2011-9-8 18:33

with t as ( select replace(sys_connect_by_path(rn,'/'),'/','') expression
            from (select rownum rn from dual connect by level <=9)
         where level=9
         connect by nocycle rn <> prior rn
      ),
   t1 as (
      select expression,
               minus_sign,
               substr(expression,1,minus_sign) AB,
               substr(expression,minus_sign+1) CD
         from t,
            (select rownum +1 minus_sign from dual connect by level <=6) a
         ),
   t2 as (
         select expression,minus_sign,first_div
         from t1,
               (select rownum first_div
                  from dual
               connect by level <= 7) b
         where minus_sign > first_div
         ),
   t3 as (
         select expression,minus_sign,first_div,second_div,
               substr(substr(expression,1,minus_sign),1,first_div)    A,
               substr(substr(expression,1,minus_sign),first_div +  1)  B,
               substr(substr(expression,minus_sign+1),1,second_div) C,
               substr(substr(expression,minus_sign+1),second_div + 1)  D
            from t2,
               (select rownum second_div
                  from dual
               connect by level <= 6) c
         where  minus_sign + second_div < 9
         )
select A,B,C,D from t3 WHERE abs(A/B - C/D) = 0

全暴力，无裁剪：绝对值最小为0，共472组。

986 2 3451 7
986 3451 2 7
984 123 56 7
984 56 123 7
98 14 532 76
98 532 14 76
98 1372 4 56
98 4 1372 56
96 12 584 73
96 584 12 73
96 174 32 58
96 32 174 58
96 1824 3 57
96 3 1824 57
96 1728 3 54
96 3 1728 54
954 1 7632 8
954 7632 1 8
953 1 7624 8
953 7624 1 8
942 7536 1 8
942 1 7536 8
932 7456 1 8
932 1 7456 8
93 186 27 54
93 27 186 54
927 3 1854 6
927 1854 3 6
92 4876 1 53
92 1 4876 53
91 2 3458 76
91 3458 2 76
9 7524 1 836
9 1 7524 836
9 153 46 782
9 46 153 782
9 327 18 654
9 18 327 654
9 1 5823 647
9 5823 1 647
9 1 5742 638
9 5742 1 638
9 1746 3 582
9 3 1746 582
9 18 273 546
9 273 18 546
9 267 18 534
9 18 267 534
9 28 153 476
9 153 28 476
897 156 23 4
897 23 156 4
87 1 5394 62
87 5394 1 62
836 1 7524 9
836 7524 1 9
8 1 7632 954
8 7632 1 954
8 1 7624 953
8 7624 1 953
8 1 7536 942
8 7536 1 942
8 1 7456 932
8 7456 1 932
8 6352 1 794
8 1 6352 794
8 46 132 759
8 132 46 759
8 1 5936 742
8 5936 1 742
8 5432 1 679
8 1 5432 679
8 5392 1 674
8 1 5392 674
8 4736 1 592
8 1 4736 592
8 4632 1 579
8 1 4632 579
8 1 4296 537
8 4296 1 537
8 1 3752 469
8 3752 1 469
8 3672 1 459
8 136 27 459
8 1 3672 459
8 27 136 459
8 2 1756 439
8 1756 2 439
8 2 1576 394
8 1576 2 394
794 1 6352 8
794 6352 1 8
793 1586 2 4
793 2 1586 4
792 3 1584 6
792 1584 3 6
79 158 32 64
79 32 158 64
79 158 23 46
79 23 158 46
782 153 46 9
782 46 153 9
769 1538 2 4
769 2 1538 4
7632 954 8 1
7632 8 954 1
7624 953 8 1
7624 8 953 1
76 14 532 98
76 532 14 98
76 2 3458 91
76 3458 2 91
759 132 46 8
759 46 132 8
7536 8 942 1
7536 942 8 1
7524 836 9 1
7524 9 836 1
7456 8 932 1
7456 932 8 1
742 1 5936 8
742 5936 1 8
74 18 259 63
74 259 18 63
73 12 584 96
73 584 12 96
73 29 146 58
73 146 29 58
729 1458 3 6
729 3 1458 6
7 3451 2 986
7 2 3451 986
7 56 123 984
7 123 56 984
7 329 14 658
7 14 329 658
7 154 29 638
7 29 154 638
7 14 293 586
7 293 14 586
7 14 269 538
7 269 14 538
7 2 1869 534
7 1869 2 534
69 23 174 58
69 174 23 58
69 138 27 54
69 27 138 54
679 1 5432 8
679 5432 1 8
679 1358 2 4
679 2 1358 4
674 1 5392 8
674 5392 1 8
67 1943 2 58
67 134 29 58
67 29 134 58
67 2 1943 58
658 14 329 7
658 329 14 7
654 18 327 9
654 327 18 9
647 1 5823 9
647 5823 1 9
64 158 32 79
64 32 158 79
638 1 5742 9
638 5742 1 9
638 154 29 7
638 29 154 7
6352 794 8 1
6352 8 794 1
63 18 259 74
63 259 18 74
62 5394 1 87
62 1 5394 87
6 1854 3 927
6 3 1854 927
6 1584 3 792
6 3 1584 792
6 1458 3 729
6 3 1458 729
6 2 1749 583
6 1749 2 583
5936 742 8 1
5936 8 742 1
592 1 4736 8
592 4736 1 8
586 14 293 7
586 293 14 7
584 73 96 12
584 96 73 12
583 1749 2 6
583 2 1749 6
5823 9 647 1
5823 647 9 1
582 3 1746 9
582 1746 3 9
58 174 32 96
58 32 174 96
58 146 29 73
58 29 146 73
58 174 23 69
58 23 174 69
58 29 134 67
58 134 29 67
58 2 1943 67
58 1943 2 67
579 1 4632 8
579 4632 1 8
5742 638 9 1
5742 9 638 1
57 1824 3 96
57 3 1824 96
56 4 1372 98
56 1372 4 98
56 984 7 123
56 7 984 123
546 18 273 9
546 273 18 9
5432 679 8 1
5432 8 679 1
54 1728 3 96
54 3 1728 96
54 186 27 93
54 27 186 93
54 138 27 69
54 27 138 69
5394 62 87 1
5394 87 62 1
5392 674 8 1
5392 8 674 1
538 14 269 7
538 269 14 7
537 4296 1 8
537 1 4296 8
534 18 267 9
534 267 18 9
534 1869 2 7
534 2 1869 7
532 76 98 14
532 98 76 14
53 1 4876 92
53 4876 1 92
4876 92 53 1
4876 53 92 1
476 153 28 9
476 28 153 9
4736 592 8 1
4736 8 592 1
469 3752 1 8
469 1 3752 8
4632 579 8 1
4632 8 579 1
46 23 158 79
46 158 23 79
46 9 782 153
46 782 9 153
46 8 759 132
46 759 8 132
459 1 3672 8
459 136 27 8
459 27 136 8
459 3672 1 8
439 2 1756 8
439 1756 2 8
4296 8 537 1
4296 537 8 1
4 23 156 897
4 156 23 897
4 1586 2 793
4 2 1586 793
4 1538 2 769
4 2 1538 769
4 1358 2 679
4 2 1358 679
4 98 56 1372
4 56 98 1372
394 2 1576 8
394 1576 2 8
3752 8 469 1
3752 469 8 1
3672 459 8 1
3672 8 459 1
3458 91 76 2
3458 76 91 2
3451 986 7 2
3451 7 986 2
329 7 658 14
329 658 7 14
327 9 654 18
327 654 9 18
32 58 96 174
32 96 58 174
32 79 64 158
32 64 79 158
3 6 927 1854
3 927 6 1854
3 96 57 1824
3 57 96 1824
3 9 582 1746
3 582 9 1746
3 96 54 1728
3 54 96 1728
3 6 792 1584
3 792 6 1584
3 729 6 1458
3 6 729 1458
293 7 586 14
293 586 7 14
29 638 7 154
29 7 638 154
29 58 73 146
29 73 58 146
29 58 67 134
29 67 58 134
28 9 476 153
28 476 9 153
273 9 546 18
273 546 9 18
27 54 93 186
27 93 54 186
27 54 69 138
27 69 54 138
27 8 459 136
27 459 8 136
269 538 7 14
269 7 538 14
267 9 534 18
267 534 9 18
259 63 74 18
259 74 63 18
23 69 58 174
23 58 69 174
23 46 79 158
23 79 46 158
23 4 897 156
23 897 4 156
2 76 91 3458
2 91 76 3458
2 986 7 3451
2 7 986 3451
2 58 67 1943
2 67 58 1943
2 534 7 1869
2 7 534 1869
2 439 8 1756
2 8 439 1756
2 583 6 1749
2 6 583 1749
2 793 4 1586
2 4 793 1586
2 8 394 1576
2 394 8 1576
2 4 769 1538
2 769 4 1538
2 679 4 1358
2 4 679 1358
1943 67 58 2
1943 58 67 2
1869 534 7 2
1869 7 534 2
186 93 54 27
186 54 93 27
1854 927 6 3
1854 6 927 3
1824 57 96 3
1824 96 57 3
18 654 9 327
18 9 654 327
18 546 9 273
18 9 546 273
18 534 9 267
18 9 534 267
18 74 63 259
18 63 74 259
1756 439 8 2
1756 8 439 2
1749 583 6 2
1749 6 583 2
1746 582 9 3
1746 9 582 3
174 96 58 32
174 58 96 32
174 58 69 23
174 69 58 23
1728 54 96 3
1728 96 54 3
1586 4 793 2
1586 793 4 2
1584 6 792 3
1584 792 6 3
158 64 79 32
158 79 64 32
158 46 79 23
158 79 46 23
1576 394 8 2
1576 8 394 2
156 4 897 23
156 897 4 23
154 638 7 29
154 7 638 29
1538 769 4 2
1538 4 769 2
153 782 9 46
153 9 782 46
153 476 9 28
153 9 476 28
146 58 73 29
146 73 58 29
1458 6 729 3
1458 729 6 3
14 76 98 532
14 98 76 532
14 7 658 329
14 658 7 329
14 586 7 293
14 7 586 293
14 7 538 269
14 538 7 269
138 69 54 27
138 54 69 27
1372 98 56 4
1372 56 98 4
136 8 459 27
136 459 8 27
1358 4 679 2
1358 679 4 2
134 58 67 29
134 67 58 29
132 8 759 46
132 759 8 46
123 7 984 56
123 984 7 56
12 96 73 584
12 73 96 584
1 954 8 7632
1 8 954 7632
1 8 953 7624
1 953 8 7624
1 942 8 7536
1 8 942 7536
1 9 836 7524
1 836 9 7524
1 932 8 7456
1 8 932 7456
1 794 8 6352
1 8 794 6352
1 8 742 5936
1 742 8 5936
1 647 9 5823
1 9 647 5823
1 9 638 5742
1 638 9 5742
1 679 8 5432
1 8 679 5432
1 87 62 5394
1 62 87 5394
1 8 674 5392
1 674 8 5392
1 53 92 4876
1 92 53 4876
1 592 8 4736
1 8 592 4736
1 8 579 4632
1 579 8 4632
1 537 8 4296
1 8 537 4296
1 8 469 3752
1 469 8 3752
1 8 459 3672
1 459 8 3672

newkid · 发表于 2011-9-8 22:08

原作者要求 "different" but closest results 也就是绝对值不能为零，我忘记把different翻译出来了。

solomon_007 · 发表于 2011-9-9 10:20

SQL> with t as ( select replace(sys_connect_by_path(rn,'/'),'/','') expression
  2             from (select rownum rn from dual connect by level <=9)
  3             where level=9
  4          connect by nocycle rn <> prior rn
  5          ),
  6    t1 as (
  7          select expression,
  8                minus_sign
  9          from t,
10                (select rownum +1 minus_sign from dual connect by level <=6) a
11          ),
12    t2 as (
13             select expression,minus_sign,first_div
14             from t1,
15                (select rownum first_div
16                   from dual
17                connect by level <= 7) b
18             where minus_sign > first_div
19          ),
20    t3 as (
21             select expression,minus_sign,first_div,second_div,
22                   substr(substr(expression,1,minus_sign),1,first_div)    A,
23                   substr(substr(expression,1,minus_sign),first_div +  1)  B,
24                   substr(substr(expression,minus_sign+1),1,second_div) C,
25                   substr(substr(expression,minus_sign+1),second_div + 1)  D
26             from t2,
27                   (select rownum second_div
28                      from dual
29                   connect by level <= 6) c
30             where  minus_sign + second_div < 9
31          ),
32    t4 as (
33          select * from t3 where  A*D > B*C
34          )
35  select A,B,C,D,A/B - C/D
36 from t4
37 where A/B - C/D = (select min(A/B - C/D) from t4 )
38  /

A       B       C    D    A/B-C/D
-------- --------- ------- ------ ---------------------
1       826    9    7435 1.62831708544268E-7

3min 45s...

sj198421 · 发表于 2011-9-9 14:41

继续膜拜下，哈哈

newkid · 发表于 2011-9-16 21:42

这个贴竟然从前天开始丢，幸亏我的浏览器缓存里还有：
#8:
Using all of the numbers once from 1 to 16, 4x4 magic squares are formed. What is the possible maximum value of the sum of four numbers in any 2x2 block on this 4x4 square.
Note: In a magic square, the numbers in all rows, all columns, and both diagonals sum to the same constant.

1-16排成4X4幻方，在这个4X4方阵中所有2X2小方阵之和的最大值是多少？
在一个幻方中所有行、列、两条对角线之和都相等。

这个难度不大。

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#50
使用道具
发表于 2011-9-15 09:19
四阶幻方：
WITH nums AS (SELECT LEVEL n, POWER(2,LEVEL-1) bit FROM DUAL CONNECT BY LEVEL<=16)
,num4 AS (
SELECT n1.n n1,n2.n n2,n3.n n3,n4.n n4
   ,n1.bit+n2.bit+n3.bit+n4.bit bit
FROM nums n1,nums n2,nums n3,nums n4
WHERE n1.n+n2.n+n3.n+n4.n=34
      AND n1.n NOT IN (n2.n,n3.n,n4.n)
      AND n2.n NOT IN (n3.n,n4.n)
      AND n3.n<>n4.n
)
,num8 AS (
SELECT n1.n1,n1.n2,n1.n3,n1.n4,n2.n1 n5,n2.n2 n6,n2.n3 n7,n2.n4 n8
   ,n1.n1+n2.n1 s1
   ,n1.n2+n2.n2 s2
   ,n1.n3+n2.n3 s3
   ,n1.n4+n2.n4 s4
   ,n1.bit+n2.bit bit
   ,n1.n1+n2.n2 d1
   ,n1.n4+n2.n3 d2
   ,n1.n3+n2.n4 d3
   ,n1.n2+n2.n1 d4
FROM num4 n1,num4 n2
WHERE BITAND(n1.bit,n2.bit)=0
)
,num16 AS (
SELECT *
FROM num8 n1,num8 n2
WHERE n1.bit = POWER(2,16)-1-n2.bit
      AND n1.s1=34 - n2.s1
      AND n1.s2=34 - n2.s2
      AND n1.s3=34 - n2.s3
      AND n1.s4=34 - n2.s4
      AND n1.d1=34 - n2.d3
      AND n1.d2=34 - n2.d4
)
SELECT count(*) FROM num16;

COUNT(*)
----------
   7040

Elapsed: 00:00:10.62

剩下的就很好办了，明天继续。

__________________

世界上只有两种编程方法：Oracle的方法和错误的方法。

剑破冰山—Oracle开发艺术即将隆重推出
http://www.china-pub.com/197199
http://www.huachu.com.cn/itbook/itbookinfo.asp?lbbh=10114321

newkid · 发表于 2011-9-16 21:45

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#51
使用道具
发表于 2011-9-15 13:45
SQL> with t as (
2          select
3                   substr(str,instr(str,'/',1, 1)+1,instr(str,'/',1, 2)-instr(str,'/',1, 1) -1) c11,
4                   substr(str,instr(str,'/',1, 2)+1,instr(str,'/',1, 3)-instr(str,'/',1, 2) -1) c12,
5                   substr(str,instr(str,'/',1, 3)+1,instr(str,'/',1, 4)-instr(str,'/',1, 3) -1) c13,
6                   substr(str,instr(str,'/',1, 4)+1,instr(str,'/',1, 5)-instr(str,'/',1, 4) -1) c21,
7                   substr(str,instr(str,'/',1, 5)+1,instr(str,'/',1, 6)-instr(str,'/',1, 5) -1) c22,
8                   substr(str,instr(str,'/',1, 6)+1,instr(str,'/',1, 7)-instr(str,'/',1, 6) -1) c23,
9                   substr(str,instr(str,'/',1, 7)+1,instr(str,'/',1, 8)-instr(str,'/',1, 7) -1) c31,
10                   substr(str,instr(str,'/',1, 8)+1,instr(str,'/',1, 9)-instr(str,'/',1, 8) -1) c32,
11                   substr(str,instr(str,'/',1, 9)+1,instr(str,'/',1,10)-instr(str,'/',1, 9) -1) c33
12             from (
13                   select sys_connect_by_path(rn,'/')||'/' str
14                   from (select rownum rn from dual connect by level <=9)
15                   where level=9
16                   connect by nocycle rn <> prior rn
17                   )
18          )
19  select *
20 from t
21 where c11 + c12 + c13 = c21 + c22 + c23
22    and c11 + c12 + c13 = c31 + c32 + c33
23    and c11 + c12 + c13 = c11 + c21 + c31
24    and c11 + c12 + c13 = c12 + c22 + c32
25    and c11 + c12 + c13 = c13 + c23 + c33
26    and c11 + c12 + c13 = c11 + c22 + c33
27    and c11 + c12 + c13 = c31 + c22 + c13
28  /

C11 C12 C13 C21 C22 C23 C31 C32 C33
--- --- --- --- --- --- --- --- ---
2 7 6 9 5 1 4 3 8
2 9 4 7 5 3 6 1 8
4 3 8 9 5 1 2 7 6
4 9 2 3 5 7 8 1 6
6 1 8 7 5 3 2 9 4
6 7 2 1 5 9 8 3 4
8 1 6 3 5 7 4 9 2
8 3 4 1 5 9 6 7 2

我上面的方法只能找3阶幻方，4阶 16! 这个太大了，跑不出来。。。

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#52
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发表于 2011-9-15 16:29
看明白了， NEWKID 用的是每4个=34的数据为单位进行填充的，4 join 4 得8 ,8 join 8 得16 ,高!

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#53
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发表于 2011-9-15 16:42

QUOTE:
原帖由 newkid 于 2011-9-14 22:03 发表
#8:
Using all of the numbers once from 1 to 16, 4x4 magic squares are formed. What is the possible maximum value of the sum of four numbers in any 2x2 block on this 4x4 square.
Note: In a magic square, the numbers in all rows, all columns, and both diagonals sum to the same constant.

1-16排成4X4幻方，在这个4X4方阵中所有2X2小方阵之和的最大值是多少？
在一个幻方中所有行、列、两条对角线之和都相等。

这个难度不大。

所有2X2小方阵之和的最大值:是否需要列举所有的幻方才能，还是有什么理论

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#54
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发表于 2011-9-15 17:20
采用newkid的：

with nums  as (select level n, power(2,level-1) bit from dual connect by level<=16),
   num4  as (
               select n1.n n1,
                     n2.n n2,
                     n3.n n3,
                     n4.n n4,
                     n1.bit+n2.bit+n3.bit+n4.bit bit
               from nums n1,
                     nums n2,
                     nums n3,
                     nums n4
               where n1.n+n2.n+n3.n+n4.n=34
               and n1.n not in (n2.n,n3.n,n4.n)
               and n2.n not in (n3.n,n4.n)
               and n3.n<>n4.n
            ),
   num8 as (
            select n1.n1,n1.n2,n1.n3,n1.n4,n2.n1 n5,n2.n2 n6,n2.n3 n7,n2.n4 n8
                  ,n1.n1+n2.n1 s1
                  ,n1.n2+n2.n2 s2
                  ,n1.n3+n2.n3 s3
                  ,n1.n4+n2.n4 s4
                  ,n1.bit+n2.bit bit
                  ,n1.n1+n2.n2 d1
                  ,n1.n4+n2.n3 d2
                  ,n1.n3+n2.n4 d3
                  ,n1.n2+n2.n1 d4
               from num4 n1,
                  num4 n2
            where bitand(n1.bit,n2.bit)=0
            ),
   num16 as (
            select n1.n1 c11,
                  n1.n2 c12,
                  n1.n3 c13,
                  n1.n4 c14,
                  n1.n5 c21,
                  n1.n6 c22,
                  n1.n7 c23,
                  n1.n8 c24,
                  n2.n1 c31,
                  n2.n2 c32,
                  n2.n3 c33,
                  n2.n4 c34,
                  n2.n5 c41,
                  n2.n6 c42,
                  n2.n7 c43,
                  n2.n8 c44
               from num8 n1,
                  num8 n2
            where n1.bit = power(2,16) - 1 - n2.bit
               and n1.s1 = 34 - n2.s1
               and n1.s2 = 34 - n2.s2
               and n1.s3 = 34 - n2.s3
               and n1.s4 = 34 - n2.s4
               and n1.d1 = 34 - n2.d3
               and n1.d2 = 34 - n2.d4
            ),
   res as (
            select c11,c12,c13,c14,c21,c22,c23,c24,c31,c32,c33,c34,c41,c42,c43,c44,
                  (c11+c12+c21+c22)+(c12+c13+c22+c23)+(c13+c14+c23+c24)
                  +(c21+c22+c31+c32)+(c22+c23+c32+c33)+(c23+c24+c33+c34)
                  +(c31+c32+c41+c42)+(c32+c33+c42+c43)+(c33+c34+c43+c44) s
               from num16
            )
select *
from (select t.*,dense_rank() over(order by s) rk from res t)
where rk = 1
;

1       8       11       6       9       12       7       10       5       1       2       15       16       13       14       3       4       306       1
2       7       6       11       10       14       9       8       3       1       4       13       16       12       15       2       5       306       1
3       12       9       8       5       6       7       10       11       1       4       13       16       15       14       3       2       306       1
4       8       5       12       9       10       11       6       7       1       4       13       16       15       14       3       2       306       1
5       12       9       6       7       8       5       10       11       1       4       15       14       13       16       3       2       306       1
6       8       5       10       11       12       9       6       7       1       4       15       14       13       16       3       2       306       1
7       10       11       7       6       8       5       9       12       1       4       16       13       15       14       2       3
               306       1

.......

(7040 组 )

是定值，恒等于306

[ 本帖最后由 solomon_007 于 2011-9-15 17:23 编辑 ]

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猫言猫语：
            人生无非是笑笑人家,再被人家笑笑而已.
            男人是用来靠的,所以要可靠;女人是用来爱的,所以要可爱.
            发怒一分钟便失去六十秒的幸福.
            人品就象内裤,表面看不出来,如果你没有还显摆,就挺讨厌.
            ......
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