Comments on: How to solve the Largest 7-Digit Number Puzzle in SQL

By: newkid

newkid — Thu, 24 Jun 2010 18:47:15 +0000

my post got messed up again. try:

WITH n AS (SELECT ROWNUM-1 n FROM DUAL CONNECT BY ROWNUM<=10)
,t(d1,d2,d3,d4,d5,d6,d7,num,lvl) AS (
SELECT n,0,0,0,0,0,0,TO_CHAR(n),1 FROM n
UNION ALL
SELECT d1
      ,DECODE(lvl,1,n,d2)
      ,DECODE(lvl,2,n,d3)
      ,DECODE(lvl,3,n,d4)
      ,DECODE(lvl,4,n,d5)
      ,DECODE(lvl,5,n,d6)
      ,DECODE(lvl,6,n,d7)
      ,CAST(n||num AS VARCHAR2(7))
      ,lvl+1
  FROM t,n
 WHERE INSTR(TO_CHAR(num),TO_CHAR(n))=0
       AND lvl<8
       AND (n=5 AND d1 IN (0,5)
            OR n IN (1,3,7,9)
            OR n IN (2,6) AND d1 IN (2,4,6,8,0)
            OR n=4 AND d1 IN (2,4,6,8,0) AND (lvl=1
                                              OR MOD(d2*10+d1,4)=0
                                              )
            OR n=8 AND d1 IN (2,4,6,8,0) AND (lvl=1
                                              OR lvl=2 AND MOD(n*1000+d2*10+d1,8)=0
                                              OR lvl NOT IN (1,2) AND MOD(d3*1000+d2*10+d1,8)=0
                                              )
            )
)
SELECT * FROM (
SELECT num FROM t 
 WHERE lvl=7 
       AND MOD(num,d1)=0 AND MOD(num,d2)=0 AND MOD(num,d3)=0 AND MOD(num,d4)=0 AND MOD(num,d5)=0
       AND MOD(num,d6)=0 AND MOD(num,d7)=0
ORDER BY num DESC
)
WHERE ROWNUM=1;

NUM
----------------------------------------
9781632

By: newkid

newkid — Thu, 24 Jun 2010 18:42:12 +0000

Something is wrong with this site. The correct SQL should be:

WITH n AS (SELECT ROWNUM-1 n FROM DUAL CONNECT BY ROWNUM<=10)
,t(d1,d2,d3,d4,d5,d6,d7,num,lvl) AS (
SELECT n,0,0,0,0,0,0,TO_CHAR(n),1 FROM n
UNION ALL
SELECT d1
,DECODE(lvl,1,n,d2)
,DECODE(lvl,2,n,d3)
,DECODE(lvl,3,n,d4)
,DECODE(lvl,4,n,d5)
,DECODE(lvl,5,n,d6)
,DECODE(lvl,6,n,d7)
,CAST(n||num AS VARCHAR2(7))
,lvl+1
FROM t,n
WHERE INSTR(TO_CHAR(num),TO_CHAR(n))=0
AND lvl2 AND MOD(d3*1000+d2*10+d1,8)=0
)
)
)
SELECT * FROM (
SELECT num FROM t
WHERE lvl=7
AND MOD(num,d1)=0 AND MOD(num,d2)=0 AND MOD(num,d3)=0 AND MOD(num,d4)=0 AND MOD(num,d5)=0
AND MOD(num,d6)=0 AND MOD(num,d7)=0
ORDER BY num DESC
)
WHERE ROWNUM=1;

By: newkid

newkid — Thu, 24 Jun 2010 18:39:54 +0000

I think there's a bug in your code:
		  WHEN n in (4)
		  THEN CASE WHEN MOD(to_number(PRIOR N||N), n) = 0 THEN 1 END
WHEN LEVEL=2, this sould be: MOD(to_number(N||PRIOR N), n) = 0
WHEN LEVEL=3, this sould be: MOD(to_number(PRIOR N||CONNECT_BY_ROOT(n)), n) = 0

Mine in 11GR2:
WITH n AS (SELECT ROWNUM-1 n FROM DUAL CONNECT BY ROWNUM<=10)
,t(d1,d2,d3,d4,d5,d6,d7,num,lvl) AS (
SELECT n,0,0,0,0,0,0,TO_CHAR(n),1 FROM n
UNION ALL
SELECT d1
      ,DECODE(lvl,1,n,d2)
      ,DECODE(lvl,2,n,d3)
      ,DECODE(lvl,3,n,d4)
      ,DECODE(lvl,4,n,d5)
      ,DECODE(lvl,5,n,d6)
      ,DECODE(lvl,6,n,d7)
      ,CAST(n||num AS VARCHAR2(7))
      ,lvl+1
  FROM t,n
 WHERE INSTR(TO_CHAR(num),TO_CHAR(n))=0
       AND lvl2 AND MOD(d3*1000+d2*10+d1,8)=0
                                              )
            )
)
SELECT * FROM (
SELECT num FROM t 
 WHERE lvl=7 
       AND MOD(num,d1)=0 AND MOD(num,d2)=0 AND MOD(num,d3)=0 AND MOD(num,d4)=0 AND MOD(num,d5)=0
       AND MOD(num,d6)=0 AND MOD(num,d7)=0
ORDER BY num DESC
)
WHERE ROWNUM=1;


NUM
----------------------------------------
9781632