Puzzle : Generating two unique numbers from an array of numbers (repetation not allowed)

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Puzzle : Generating two unique numbers from an array of numbers (repetation not allowed)

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Shaun-884394

Posted Wednesday, September 12, 2012 7:19 AM

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Hi All,

(This is just for fun, so you may choose to ignore this topic.)

Today I read a puzzle somewhere which is mentioned below.
I thought why not solve it by some SQL query.

Puzzle : Use the numbers 1,2,3,4,5,6,7,8,9 only once to fill in the blanks and complete the equation.
(4 _ _ _ 6) - (_ _ _ _) = 33333

As you see for the equation we have to generate 2 numbers, first a 3 digit number and second a 4 digit number and none of the digits in both these numbers can be repeated.

So here is the query i tried and it worked fine.
But i was wondering whether the negation joins i have used is the only way to achieve this?
Is there any smarter/efficient way to crack this puzzle?

with a(num) as
(select 1 union select 2 union select 3 union select 4 union select 5 union select 6 union select 7 union select 8 union select 9)
,b(num1,num2) as
(
	select
		convert(bigint, '4' + convert(varchar,a.num) + convert(varchar,b.num) + convert(varchar,c.num) + '6')
		,convert(bigint, convert(varchar,d.num) + convert(varchar,e.num) + convert(varchar,f.num) + convert(varchar,g.num))
	from
		a
		join a as b on a.num <> b.num
		join a as c on a.num <> b.num and a.num <> c.num
					and b.num <> c.num
		join a as d on a.num <> b.num and a.num <> c.num and a.num <> d.num 
					and b.num <> c.num and b.num <> d.num 
					and c.num <> d.num
		join a as e on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num
					and c.num <> d.num and c.num <> e.num
					and d.num <> e.num
		join a as f on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num and a.num <> f.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num and b.num <> f.num
					and c.num <> d.num and c.num <> e.num and c.num <> f.num
					and d.num <> e.num and d.num <> f.num
					and e.num <> f.num
		join a as g on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num and a.num <> f.num and a.num <> g.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num and b.num <> f.num and b.num <> g.num
					and c.num <> d.num and c.num <> e.num and c.num <> f.num and c.num <> g.num
					and d.num <> e.num and d.num <> f.num and d.num <> g.num
					and e.num <> f.num and e.num <> g.num
					and f.num <> g.num
)
select * from b 
where num1-num2 = 33333
order by 1,2

Post #1357963

Eugene Elutin

Posted Wednesday, September 12, 2012 7:43 AM

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You don't really need last join as the last digit of the second number can only be '3'

with a(num) as
(select 1 union select 2 union select 4 union select 5 union select 6 union select 7 union select 8 union select 9)
,b(num1,num2) as
(
	select
		convert(bigint, '4' + convert(varchar,a.num) + convert(varchar,b.num) + convert(varchar,c.num) + '6')
		,convert(bigint, convert(varchar,d.num) + convert(varchar,e.num) + convert(varchar,f.num) + '3')
	from
		a
		join a as b on a.num <> b.num
		join a as c on a.num <> b.num and a.num <> c.num
					and b.num <> c.num
		join a as d on a.num <> b.num and a.num <> c.num and a.num <> d.num 
					and b.num <> c.num and b.num <> d.num 
					and c.num <> d.num
		join a as e on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num
					and c.num <> d.num and c.num <> e.num
					and d.num <> e.num
		join a as f on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num and a.num <> f.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num and b.num <> f.num
					and c.num <> d.num and c.num <> e.num and c.num <> f.num
					and d.num <> e.num and d.num <> f.num
					and e.num <> f.num
)
select distinct *,  num1-num2  from b 
where num1-num2 = 33333
order by 1,2

Also, I thought that you shouldn't be able to use 4 and 6 as they were already used by the first number. In this case you will get only single possible result:

with a(num) as
(select 1 union select 2 union select 5 union select 7 union select 8 union select 9)
,b(num1,num2) as
(
	select
		convert(bigint, '4' + convert(varchar,a.num) + convert(varchar,b.num) + convert(varchar,c.num) + '6')
		,convert(bigint, convert(varchar,d.num) + convert(varchar,e.num) + convert(varchar,f.num) + '3')
	from
		a
		join a as b on a.num <> b.num
		join a as c on a.num <> b.num and a.num <> c.num
					and b.num <> c.num
		join a as d on a.num <> b.num and a.num <> c.num and a.num <> d.num 
					and b.num <> c.num and b.num <> d.num 
					and c.num <> d.num
		join a as e on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num
					and c.num <> d.num and c.num <> e.num
					and d.num <> e.num
		join a as f on a.num <> b.num and a.num <> c.num and a.num <> d.num and a.num <> e.num and a.num <> f.num
					and b.num <> c.num and b.num <> d.num and b.num <> e.num and b.num <> f.num
					and c.num <> d.num and c.num <> e.num and c.num <> f.num
					and d.num <> e.num and d.num <> f.num
					and e.num <> f.num
)
select distinct *,  num1-num2  from b 
where num1-num2 = 33333
order by 1,2

_____________________________________________
"The only true wisdom is in knowing you know nothing"
"O skol'ko nam otkrytiy chudnyh prevnosit microsofta duh!" BigGrin

(So many miracle inventions provided by MS to us...)

How to post your question to get the best and quick help

Post #1357974

Eugene Elutin

Posted Wednesday, September 12, 2012 7:52 AM

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Last Login: Yesterday @ 9:40 AM
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Also, you don't need to check if the same digits from different joins are not equal (eg. if checked a.num<>b.num in one "join" you don't need to check it again in other "joins"). Therefore all JOINs can be rewritten using "incremented" NOT IN:


with a(num) as
(select 1 union select 2 union select 5 union select 7 union select 8 union select 9)
,b(num1,num2) as
(
	select
		convert(bigint, '4' + convert(varchar,a.num) + convert(varchar,b.num) + convert(varchar,c.num) + '6')
		,convert(bigint, convert(varchar,d.num) + convert(varchar,e.num) + convert(varchar,f.num) + '3')
	from
		a
		join a as b on a.num <> b.num
		join a as c on c.num NOT IN (a.num, b.num)
		join a as d on d.num NOT IN (a.num, b.num, c.num)
		join a as e on e.num NOT IN (a.num, b.num, c.num, d.num)
		join a as f on f.num NOT IN (a.num, b.num, c.num, d.num, e.num)
)
select distinct *,  num1-num2  from b 
where num1-num2 = 33333
order by 1,2

_____________________________________________
"The only true wisdom is in knowing you know nothing"
"O skol'ko nam otkrytiy chudnyh prevnosit microsofta duh!" BigGrin

(So many miracle inventions provided by MS to us...)

How to post your question to get the best and quick help

Post #1357980

GSquared

Posted Wednesday, September 12, 2012 7:58 AM

SSCoach

Group: General Forum Members
Last Login: Monday, June 17, 2013 1:45 PM
Points: 15,442, Visits: 9,572

Here's what I came up with. Does the same thing the same way, just another way to write it:

WITH    Numbers
          AS (SELECT    *
              FROM      ( VALUES ( '1'), ( '2'), ( '3'), ( '4'), ( '5'), ( '6'), ( '7'), ( '8'), ( '9') ) AS Nums (Number))
    SELECT  N1.Number + N2.Number + N3.Number + N4.Number + N5.Number, N6.Number + N7.Number + N8.Number + N9.Number
    FROM    Numbers AS N1
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N2
                         WHERE  N2.Number != N1.Number) AS N2
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N3
                         WHERE  N3.Number NOT IN (N1.Number, N2.Number)) AS N3
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N4
                         WHERE  N4.Number NOT IN (N1.Number, N2.Number, N3.Number)) AS N4
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N5
                         WHERE  N5.Number NOT IN (N1.Number, N2.Number, N3.Number, N4.Number)) AS N5
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N6
                         WHERE  N6.Number NOT IN (N1.Number, N2.Number, N3.Number, N4.Number, N5.Number)) AS N6
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N7
                         WHERE  N7.Number NOT IN (N1.Number, N2.Number, N3.Number, N4.Number, N5.Number, N6.Number)) AS N7
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N8
                         WHERE  N8.Number NOT IN (N1.Number, N2.Number, N3.Number, N4.Number, N5.Number, N6.Number,
                                                  N7.Number)) AS N8
            CROSS APPLY (SELECT Number
                         FROM   Numbers AS N9
                         WHERE  N9.Number NOT IN (N1.Number, N2.Number, N3.Number, N4.Number, N5.Number, N6.Number,
                                                  N7.Number, N8.Number)) AS N9
    WHERE   N1.Number = '4'
            AND N5.Number = '6'
            AND CAST(N1.Number + N2.Number + N3.Number + N4.Number + N5.Number AS INT)
            - CAST(N6.Number + N7.Number + N8.Number + N9.Number AS INT) = 33333

- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread

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Post #1357989

Eugene Elutin

Posted Wednesday, September 12, 2012 8:06 AM

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Last Login: Yesterday @ 9:40 AM
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As said before, you don't need to guess the last digit of the second number as it can be only 3!
Saves one cross-apply...

_____________________________________________
"The only true wisdom is in knowing you know nothing"
"O skol'ko nam otkrytiy chudnyh prevnosit microsofta duh!" BigGrin

(So many miracle inventions provided by MS to us...)

How to post your question to get the best and quick help

Post #1357995

Luis Cazares

Posted Wednesday, September 12, 2012 8:22 AM

Ten Centuries

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Points: 1,091, Visits: 2,205

Eugene Elutin (9/12/2012)

You don't really need last join as the last digit of the second number can only be '3'

Wouldn't that be cheating?
Because that way I can get the best performance

SELECT 41286 num1,
	7953 num2

I had my solution that was very similar to yours (again) but using the different(<>) operators instead of the NOT IN.

However, a better performance would be using the best datatype for the digits (char) since the beginning avoiding additional conversions.

Luis C.
Please don't trust me, test the solutions I give you before using them.
Forum Etiquette: How to post data/code on a forum to get the best help

Post #1358004

Shaun-884394

Posted Wednesday, September 12, 2012 8:23 AM

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Group: General Forum Members
Last Login: Monday, April 22, 2013 2:32 AM
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Thank you Eugene and GSquared.

Eugene, the NOT IN looks like a much better/easier/readable join.

GSquared i love your signature ROFL,LOL,ETC .... BigGrin

I don't think it can get any better.

Post #1358006

Eugene Elutin

Posted Wednesday, September 12, 2012 8:39 AM

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Group: General Forum Members
Last Login: Yesterday @ 9:40 AM
Points: 2,596, Visits: 4,507

Luis Cazares (9/12/2012)

Eugene Elutin (9/12/2012)

You don't really need last join as the last digit of the second number can only be '3'

Wouldn't that be cheating?
....

Cheating? No, it's a common sense. There is no other number you can deduct from 6 to get 3. There is no need to guess that.
Regarding performance... I don't think it is relevant to this kind of task at all.
I guess finding the more "elegant" looking solution is what OP is after.
Saying that, removing number of casting will make it look more elegant:


;with a (num)
as
( select * from (values ('1'),('2'),('5'),('7'),('8'),('9')) a(num) )
,b 
as
(
    select  '4' + a.num + b.num + c.num + '6' as num1
           ,d.num + e.num + f.num + '3'       as num2
    from a
    join a as b on a.num <> b.num
    join a as c on c.num NOT IN (a.num, b.num)
    join a as d on d.num NOT IN (a.num, b.num, c.num)
    join a as e on e.num NOT IN (a.num, b.num, c.num, d.num)
    join a as f on f.num NOT IN (a.num, b.num, c.num, d.num, e.num)
)
select * from b 
where cast(num1 as int) - cast(num2 as int)= 33333

_____________________________________________
"The only true wisdom is in knowing you know nothing"
"O skol'ko nam otkrytiy chudnyh prevnosit microsofta duh!" BigGrin

(So many miracle inventions provided by MS to us...)

How to post your question to get the best and quick help

Post #1358013

GSquared

Posted Wednesday, September 12, 2012 8:42 AM

SSCoach

Group: General Forum Members
Last Login: Monday, June 17, 2013 1:45 PM
Points: 15,442, Visits: 9,572

Luis Cazares (9/12/2012)

Eugene Elutin (9/12/2012)

You don't really need last join as the last digit of the second number can only be '3'

Wouldn't that be cheating?
Because that way I can get the best performance

SELECT 41286 num1,
	7953 num2

I had my solution that was very similar to yours (again) but using the different(<>) operators instead of the NOT IN.

However, a better performance would be using the best datatype for the digits (char) since the beginning avoiding additional conversions.

(emphasis added)

That's why I did mine that way. Makes the concatenation, etc., more efficient, at the cost of the final Where clause being slightly more costly.

I also kept the rules for what fixed numbers go in what columns in the Where clause, instead of in the various From objects, because that way it can be modified for related queries more easily. If, for example, the puzzle were modified to "second number must start with '79'" instead of "first number must start with '4' and end with '6'", then a simple modification of the Where clause would make my version work.

For related puzzles, you could assign a parameter to each column. If not null, then fixed value for that column. Final value could also be a parameter.

And, yeah, I really do think extensibility like that with every piece of code I write.

- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread

"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon

Post #1358017

GSquared

Posted Wednesday, September 12, 2012 8:44 AM

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Group: General Forum Members
Last Login: Monday, June 17, 2013 1:45 PM
Points: 15,442, Visits: 9,572

Shaun-884394 (9/12/2012)

...

GSquared i love your signature ROFL,LOL,ETC .... BigGrin

I don't think it can get any better.

Thanks!

The really funny part is, there was a noticable increase in people assuming my posts were credible, when I added all that to my sig.

- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread

"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon

Post #1358019

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