MS SQL Server for logical conclusion

Did you know that MS SQL Server optimization techniques are so good that you can even use it to walk through millions and billions and trillions of possible solutions to find the correct one?

Let me show how this works on a very simple (for a computer) sample. It is one of those mind blowing self-referring tests which can be found on the BrainBashers site:

1. The first question with B as the correct answer is: 
A. 1   B. 4   C. 3   D. 2   

2. The answer to Question 4 is: 
A. D   B. A   C. B   D. C

3. The answer to Question 1 is: 
A. D   B. C   C. B   D. A

4. The number of questions which have D as the correct answer is: 
A. 3   B. 2   C. 1   D. 0

5. The number of questions which have B as the correct answer is: 
A. 0   B. 2   C. 3  D. 1

We will use Common Table Expressions for the query, which is a really great tool for complex queries. We do not even need real tables to work with, we will create all the data needed in the select query itself.

For a start let's get all the possible solutions for this puzzle. Here is the query:

with t as
(select 'A' as a
union
select 'B'
union
select 'C'
union
select 'D')
select  *
from t as t1, t as t2, t as t3, t as t4, t as t5 /* Cross join */

Here we create list of the letters 'A', 'B', 'C' and 'D' which is possible answers for a single questions and join those letters with themselves five times to get all possible combinations:

This is good, but not good enough since we need only the right answer, not all of them. So let's add filter expressions in the WHERE clause.

And we have basically filter expressions, one for each questions of the puzzle. Let's take the first question and translate it to SQL.

1. The first question with B as the correct answer is: 
A. 1   B. 4   C. 3   D. 2  

In SQL it will be very simple. We need to check all possible answers to the first question and ensure that the 'B' answer does not come before the given option:

(t1.a='A' and t1.a='B' --false)
or (t1.a='B' and t4.a='B' --false)
or (t1.a='C' and t3.a='B' and t1.a!='B' and t2.a!='B')
or (t1.a='D' and t2.a='B' and t1.a!='B' )

The two first options are obviously false but let's keep them anyway. SQL Server should figure that by itself.

The second questions is even more straightforward. We need to bind the 2nd and the 4th questions:

 (t2.a='A' and t4.a='D')
or (t2.a='B' and t4.a='A')
or (t2.a='C' and t4.a='B')
or (t2.a='D' and t4.a='C')

You get the idea. Let me show the final SQL for this puzzle:

with t as
(select 'A' as a
union
select 'B'
union
select 'C'
union
select 'D')
select  *
  from t as t1, t as t2, t as t3, t as t4, t as t5 /* Cross join */
where
( -- 1
   (t1.a='A' and t1.a='B')
or (t1.a='B' and t4.a='B' --false)
or (t1.a='C' and t3.a='B' and t1.a!='B' and t2.a!='B')
or (t1.a='D' and t2.a='B' and t1.a!='B' )
)
and
( -- 2
   (t2.a='A' and t4.a='D')
or (t2.a='B' and t4.a='A')
or (t2.a='C' and t4.a='B')
or (t2.a='D' and t4.a='C')
)
and
( -- 3
   (t3.a='A' and t1.a='D')
or (t3.a='B' and t1.a='C')
or (t3.a='C' and t1.a='B')
or (t3.a='D' and t1.a='A')
)
and
( -- 4
   (t4.a='A' and	3=(case when t1.a = 'D' then 1 else 0 end
          +case when t2.a = 'D' then 1 else 0 end
          +case when t3.a = 'D' then 1 else 0 end
          +case when t4.a = 'D' then 1 else 0 end
          +case when t5.a = 'D' then 1 else 0 end))
or (t4.a='B' and 2=(case when t1.a = 'D' then 1 else 0 end
          +case when t2.a = 'D' then 1 else 0 end
          +case when t3.a = 'D' then 1 else 0 end
          +case when t4.a = 'D' then 1 else 0 end
          +case when t5.a = 'D' then 1 else 0 end))
or (t4.a='C' and 1=(case when t1.a = 'D' then 1 else 0 end
          +case when t2.a = 'D' then 1 else 0 end
          +case when t3.a = 'D' then 1 else 0 end
          +case when t4.a = 'D' then 1 else 0 end
          +case when t5.a = 'D' then 1 else 0 end))
or (t4.a='D' and 0=(case when t1.a = 'D' then 1 else 0 end
          +case when t2.a = 'D' then 1 else 0 end
          +case when t3.a = 'D' then 1 else 0 end
          +case when t4.a = 'D' then 1 else 0 end
          +case when t5.a = 'D' then 1 else 0 end))
)
and
( -- 5
(t5.a='A' and	0=(case when t1.a = 'B' then 1 else 0 end
          +case when t2.a = 'B' then 1 else 0 end
          +case when t3.a = 'B' then 1 else 0 end
          +case when t4.a = 'B' then 1 else 0 end
          +case when t5.a = 'B' then 1 else 0 end))
or (t5.a='B' and 2=(case when t1.a = 'B' then 1 else 0 end
          +case when t2.a = 'B' then 1 else 0 end
          +case when t3.a = 'B' then 1 else 0 end
          +case when t4.a = 'B' then 1 else 0 end
          +case when t5.a = 'B' then 1 else 0 end))
or (t5.a='C' and 3=(case when t1.a = 'B' then 1 else 0 end
          +case when t2.a = 'B' then 1 else 0 end
          +case when t3.a = 'B' then 1 else 0 end
          +case when t4.a = 'B' then 1 else 0 end
          +case when t5.a = 'B' then 1 else 0 end))
or (t5.a='D' and 1=(case when t1.a = 'B' then 1 else 0 end
          +case when t2.a = 'B' then 1 else 0 end
          +case when t3.a = 'B' then 1 else 0 end
          +case when t4.a = 'B' then 1 else 0 end
          +case when t5.a = 'B' then 1 else 0 end))
)

And running this query gives us the answer in no time: 'C D B C B'.

But it is only 1024 variants. Let's try something harder!
How about the SELF-REFERENTIAL APTITUDE TEST, by James Propp? The are 5^19 = 1.90734863 × 10^13 variants which is a pretty huge number even for modern computers. But MS SQL Server gives a solution ('DADBEDDEDABADBADBABE') in less than a second.

The querry is 20kB long but really easy to construct since it is the same questions in the form of SQL:

with t as
(select 1 as a
union
select 2
union
select 3
union
select 4
union
select 5)
select  *
  from t as t1, t as t2, t as t3, t as t4, t as t5,
                    t as t6, t as t7, t as t8, t as t9, t as t10,
                    t as t11, t as t12, t as t13, t as t14, t as t15,
                    t as t16, t as t17, t as t18, t as t19, (select 5 as a) as t20 /* Cross join */
where 
(
(t1.a = 2 and t2.a = 2)
or (t1.a = 3 and t3.a = 2)
or (t1.a = 4 and t4.a = 2)
or (t1.a = 5 and t5.a = 2)
) /* 1 */
and
(
(t2.a = 1 and (t6.a = t7.a)
and (t1.a != t2.a) and (t2.a != t3.a) and (t4.a != t5.a) and (t5.a != t6.a)
/*and (t6.a != t7.a)*/ and (t7.a != t8.a) and (t8.a != t9.a) and (t9.a != t10.a)
and (t10.a != t11.a) and (t11.a != t12.a) and (t12.a != t13.a) and (t13.a != t14.a)
and (t14.a != t15.a) and (t15.a != t16.a) and (t16.a != t17.a) and (t17.a != t18.a) 
 and (t18.a != t19.a) and (t19.a != t20.a))
 or (t2.a = 2 and (t7.a = t8.a)
and (t1.a != t2.a) and (t2.a != t3.a) and (t4.a != t5.a) and (t5.a != t6.a)
and (t6.a != t7.a)/* and (t7.a != t8.a)*/ and (t8.a != t9.a) and (t9.a != t10.a)
and (t10.a != t11.a) and (t11.a != t12.a) and (t12.a != t13.a) and (t13.a != t14.a)
and (t14.a != t15.a) and (t15.a != t16.a) and (t16.a != t17.a) and (t17.a != t18.a) 
 and (t18.a != t19.a) and (t19.a != t20.a)
)
or (t2.a = 3 and (t8.a = t9.a)
and (t1.a != t2.a) and (t2.a != t3.a) and (t4.a != t5.a) and (t5.a != t6.a)
and (t6.a != t7.a) and (t7.a != t8.a)/* and (t8.a != t9.a)*/ and (t9.a != t10.a)
and (t10.a != t11.a) and (t11.a != t12.a) and (t12.a != t13.a) and (t13.a != t14.a)
and (t14.a != t15.a) and (t15.a != t16.a) and (t16.a != t17.a) and (t17.a != t18.a) 
 and (t18.a != t19.a) and (t19.a != t20.a))
or (t2.a = 4 and (t9.a = t10.a)
and (t1.a != t2.a) and (t2.a != t3.a) and (t4.a != t5.a) and (t5.a != t6.a)
and (t6.a != t7.a) and (t7.a != t8.a) and (t8.a != t9.a) /*and (t9.a != t10.a)*/
and (t10.a != t11.a) and (t11.a != t12.a) and (t12.a != t13.a) and (t13.a != t14.a)
and (t14.a != t15.a) and (t15.a != t16.a) and (t16.a != t17.a) and (t17.a != t18.a) 
 and (t18.a != t19.a) and (t19.a != t20.a)
)
or (t2.a = 5 and (T10.a = t11.a)
and (t1.a != t2.a) and (t2.a != t3.a) and (t4.a != t5.a) and (t5.a != t6.a)
and (t6.a != t7.a) and (t7.a != t8.a) and (t8.a != t9.a) and (t9.a != t10.a)
/*and (t10.a != t11.a)*/ and (t11.a != t12.a) and (t12.a != t13.a) and (t13.a != t14.a)
and (t14.a != t15.a) and (t15.a != t16.a) and (t16.a != t17.a) and (t17.a != t18.a) 
 and (t18.a != t19.a) and (t19.a != t20.a)
)
) /* 2 */ 
and
(
  t3.a = 1 + (case when t1.a = 5 then 1 else 0 end
+ case when t2.a = 5 then 1 else 0 end
+ case when t3.a = 5 then 1 else 0 end
+ case when t4.a = 5 then 1 else 0 end
+ case when t5.a = 5 then 1 else 0 end
+ case when t6.a = 5 then 1 else 0 end
+ case when t7.a = 5 then 1 else 0 end
+ case when t8.a = 5 then 1 else 0 end
+ case when t9.a = 5 then 1 else 0 end
+ case when t10.a = 5 then 1 else 0 end
+ case when t11.a = 5 then 1 else 0 end
+ case when t12.a = 5 then 1 else 0 end
+ case when t13.a = 5 then 1 else 0 end
+ case when t14.a = 5 then 1 else 0 end
+ case when t15.a = 5 then 1 else 0 end
+ case when t16.a = 5 then 1 else 0 end
+ case when t17.a = 5 then 1 else 0 end
+ case when t18.a = 5 then 1 else 0 end
+ case when t19.a = 5 then 1 else 0 end
+ case when t20.a = 5 then 1 else 0 end) 
) /* 3 */
and
(
t4.a + 3 = (case when t1.a = 1 then 1 else 0 end
+ case when t2.a = 1 then 1 else 0 end
+ case when t3.a = 1 then 1 else 0 end
+ case when t4.a = 1 then 1 else 0 end
+ case when t5.a = 1 then 1 else 0 end
+ case when t6.a = 1 then 1 else 0 end
+ case when t7.a = 1 then 1 else 0 end
+ case when t8.a = 1 then 1 else 0 end
+ case when t9.a = 1 then 1 else 0 end
+ case when t10.a = 1 then 1 else 0 end
+ case when t11.a = 1 then 1 else 0 end
+ case when t12.a = 1 then 1 else 0 end
+ case when t13.a = 1 then 1 else 0 end
+ case when t14.a = 1 then 1 else 0 end
+ case when t15.a = 1 then 1 else 0 end
+ case when t16.a = 1 then 1 else 0 end
+ case when t17.a = 1 then 1 else 0 end
+ case when t18.a = 1 then 1 else 0 end
+ case when t19.a = 1 then 1 else 0 end
+ case when t20.a = 1 then 1 else 0 end)
) /* 4 */
and
(
(t5.a = t1.a and t1.a = 1)
or (t5.a = t2.a and t2.a = 2)
or (t5.a = t3.a and t3.a = 3)
or (t5.a = t4.a and t4.a = 4)
or (t5.a = t5.a and t5.a = 5)  
) /* 5 */
and
(
    (t6.a = 1 and t17.a = 3)
or (t6.a = 2 and t17.a = 4)
or (t6.a = 3 and t17.a = 5)
or (t6.a = 4 and not t17.a in (3, 4, 5))
) /* 6 */
and
(
(5 - t7.a) = abs(t7.a - t8.a)
) /* 7 */
and
(
  t8.a + 3 = 
  (case when t1.a in (1, 5) then 1 else 0 end
+ case when t2.a in (1, 5) then 1 else 0 end
+ case when t3.a in (1, 5) then 1 else 0 end
+ case when t4.a in (1, 5) then 1 else 0 end
+ case when t5.a in (1, 5) then 1 else 0 end
+ case when t6.a in (1, 5) then 1 else 0 end
+ case when t7.a in (1, 5) then 1 else 0 end
+ case when t8.a in (1, 5) then 1 else 0 end
+ case when t9.a in (1, 5) then 1 else 0 end
+ case when t10.a in (1, 5) then 1 else 0 end
+ case when t11.a in (1, 5) then 1 else 0 end
+ case when t12.a in (1, 5) then 1 else 0 end
+ case when t13.a in (1, 5) then 1 else 0 end
+ case when t14.a in (1, 5) then 1 else 0 end
+ case when t15.a in (1, 5) then 1 else 0 end
+ case when t16.a in (1, 5) then 1 else 0 end
+ case when t17.a in (1, 5) then 1 else 0 end
+ case when t18.a in (1, 5) then 1 else 0 end
+ case when t19.a in (1, 5) then 1 else 0 end
+ case when t20.a in (1, 5) then 1 else 0 end)
) /* 8 */
and
(
    (t9.a = 1 and t10.a = 1)
or (t9.a = 2 and t11.a = 2)
or (t9.a = 3 and t12.a = 3)
or (t9.a = 4 and t13.a = 4)
or (t9.a = 5 and t14.a = 5)
) /* 9 */
and
(
    (t10.a = 1 and t16.a = 4)
or (t10.a = 2 and t16.a = 1)
or (t10.a = 3 and t16.a = 5)
or (t10.a = 4 and t16.a = 2)
or (t10.a = 5 and t16.a = 3)
) /* 10 */
and
(
  t11.a = 1 +
(case when t1.a = 2 then 1 else 0 end
+ case when t2.a = 2 then 1 else 0 end
+ case when t3.a = 2 then 1 else 0 end
+ case when t4.a = 2 then 1 else 0 end
+ case when t5.a = 2 then 1 else 0 end
+ case when t6.a = 2 then 1 else 0 end
+ case when t7.a = 2 then 1 else 0 end
+ case when t8.a = 2 then 1 else 0 end
+ case when t9.a = 2 then 1 else 0 end
+ case when t10.a = 2 then 1 else 0 end)
) /* 11 */
and
(
(t12.a = 1 and (case when t1.a in (2, 3, 4) then 1 else 0 end
+ case when t2.a in (2, 3, 4) then 1 else 0 end
+ case when t3.a in (2, 3, 4) then 1 else 0 end
+ case when t4.a in (2, 3, 4) then 1 else 0 end
+ case when t5.a in (2, 3, 4) then 1 else 0 end
+ case when t6.a in (2, 3, 4) then 1 else 0 end
+ case when t7.a in (2, 3, 4) then 1 else 0 end
+ case when t8.a in (2, 3, 4) then 1 else 0 end
+ case when t9.a in (2, 3, 4) then 1 else 0 end
+ case when t10.a in (2, 3, 4) then 1 else 0 end
+ case when t11.a in (2, 3, 4) then 1 else 0 end
+ case when t12.a in (2, 3, 4) then 1 else 0 end
+ case when t13.a in (2, 3, 4) then 1 else 0 end
+ case when t14.a in (2, 3, 4) then 1 else 0 end
+ case when t15.a in (2, 3, 4) then 1 else 0 end
+ case when t16.a in (2, 3, 4) then 1 else 0 end
+ case when t17.a in (2, 3, 4) then 1 else 0 end
+ case when t18.a in (2, 3, 4) then 1 else 0 end
+ case when t19.a in (2, 3, 4) then 1 else 0 end
+ case when t20.a in (2, 3, 4) then 1 else 0 end) % 2 = 0
) 
 or (t1.a = 2 and (case when t1.a in (2, 3, 4) then 1 else 0 end
+ case when t2.a in (2, 3, 4) then 1 else 0 end
+ case when t3.a in (2, 3, 4) then 1 else 0 end
+ case when t4.a in (2, 3, 4) then 1 else 0 end
+ case when t5.a in (2, 3, 4) then 1 else 0 end
+ case when t6.a in (2, 3, 4) then 1 else 0 end
+ case when t7.a in (2, 3, 4) then 1 else 0 end
+ case when t8.a in (2, 3, 4) then 1 else 0 end
+ case when t9.a in (2, 3, 4) then 1 else 0 end
+ case when t10.a in (2, 3, 4) then 1 else 0 end
+ case when t11.a in (2, 3, 4) then 1 else 0 end
+ case when t12.a in (2, 3, 4) then 1 else 0 end
+ case when t13.a in (2, 3, 4) then 1 else 0 end
+ case when t14.a in (2, 3, 4) then 1 else 0 end
+ case when t15.a in (2, 3, 4) then 1 else 0 end
+ case when t16.a in (2, 3, 4) then 1 else 0 end
+ case when t17.a in (2, 3, 4) then 1 else 0 end
+ case when t18.a in (2, 3, 4) then 1 else 0 end
+ case when t19.a in (2, 3, 4) then 1 else 0 end
+ case when t20.a in (2, 3, 4) then 1 else 0 end) % 2 = 1
) 
 or (t1.a = 3 and (case when t1.a in (2, 3, 4) then 1 else 0 end
+ case when t2.a in (2, 3, 4) then 1 else 0 end
+ case when t3.a in (2, 3, 4) then 1 else 0 end
+ case when t4.a in (2, 3, 4) then 1 else 0 end
+ case when t5.a in (2, 3, 4) then 1 else 0 end
+ case when t6.a in (2, 3, 4) then 1 else 0 end
+ case when t7.a in (2, 3, 4) then 1 else 0 end
+ case when t8.a in (2, 3, 4) then 1 else 0 end
+ case when t9.a in (2, 3, 4) then 1 else 0 end
+ case when t10.a in (2, 3, 4) then 1 else 0 end
+ case when t11.a in (2, 3, 4) then 1 else 0 end
+ case when t12.a in (2, 3, 4) then 1 else 0 end
+ case when t13.a in (2, 3, 4) then 1 else 0 end
+ case when t14.a in (2, 3, 4) then 1 else 0 end
+ case when t15.a in (2, 3, 4) then 1 else 0 end
+ case when t16.a in (2, 3, 4) then 1 else 0 end
+ case when t17.a in (2, 3, 4) then 1 else 0 end
+ case when t18.a in (2, 3, 4) then 1 else 0 end
+ case when t19.a in (2, 3, 4) then 1 else 0 end
+ case when t20.a in (2, 3, 4) then 1 else 0 end) in (1, 4)
) 
 or (t1.a = 4 and (case when t1.a in (2, 3, 4) then 1 else 0 end
+ case when t2.a in (2, 3, 4) then 1 else 0 end
+ case when t3.a in (2, 3, 4) then 1 else 0 end
+ case when t4.a in (2, 3, 4) then 1 else 0 end
+ case when t5.a in (2, 3, 4) then 1 else 0 end
+ case when t6.a in (2, 3, 4) then 1 else 0 end
+ case when t7.a in (2, 3, 4) then 1 else 0 end
+ case when t8.a in (2, 3, 4) then 1 else 0 end
+ case when t9.a in (2, 3, 4) then 1 else 0 end
+ case when t10.a in (2, 3, 4) then 1 else 0 end
+ case when t11.a in (2, 3, 4) then 1 else 0 end
+ case when t12.a in (2, 3, 4) then 1 else 0 end
+ case when t13.a in (2, 3, 4) then 1 else 0 end
+ case when t14.a in (2, 3, 4) then 1 else 0 end
+ case when t15.a in (2, 3, 4) then 1 else 0 end
+ case when t16.a in (2, 3, 4) then 1 else 0 end
+ case when t17.a in (2, 3, 4) then 1 else 0 end
+ case when t18.a in (2, 3, 4) then 1 else 0 end
+ case when t19.a in (2, 3, 4) then 1 else 0 end
+ case when t20.a in (2, 3, 4) then 1 else 0 end)  in (2, 3, 5)
)
or (t1.a = 5 and (case when t1.a in (2, 3, 4) then 1 else 0 end
+ case when t2.a in (2, 3, 4) then 1 else 0 end
+ case when t3.a in (2, 3, 4) then 1 else 0 end
+ case when t4.a in (2, 3, 4) then 1 else 0 end
+ case when t5.a in (2, 3, 4) then 1 else 0 end
+ case when t6.a in (2, 3, 4) then 1 else 0 end
+ case when t7.a in (2, 3, 4) then 1 else 0 end
+ case when t8.a in (2, 3, 4) then 1 else 0 end
+ case when t9.a in (2, 3, 4) then 1 else 0 end
+ case when t10.a in (2, 3, 4) then 1 else 0 end
+ case when t11.a in (2, 3, 4) then 1 else 0 end
+ case when t12.a in (2, 3, 4) then 1 else 0 end
+ case when t13.a in (2, 3, 4) then 1 else 0 end
+ case when t14.a in (2, 3, 4) then 1 else 0 end
+ case when t15.a in (2, 3, 4) then 1 else 0 end
+ case when t16.a in (2, 3, 4) then 1 else 0 end
+ case when t17.a in (2, 3, 4) then 1 else 0 end
+ case when t18.a in (2, 3, 4) then 1 else 0 end
+ case when t19.a in (2, 3, 4) then 1 else 0 end
+ case when t20.a in (2, 3, 4) then 1 else 0 end) = 5
) 
) /* 12 */
and
(
t1.a != 1 and t3.a != 1  and t5.a != 1  and t7.a != 1 and t19.a != 1 and 
 (
     t13.a = 1 and (t9.a = 1  and t11.a != 1  and t13.a != 1 and t15.a != 1 and t17.a != 1 and t19.a != 1)
  or t13.a = 2 and (t9.a != 1  and t11.a = 1  and t13.a != 1 and t15.a != 1 and t17.a != 1 and t19.a != 1)
  or t13.a = 3 and (t9.a != 1  and t11.a != 1  and t13.a = 1 and t15.a != 1 and t17.a != 1 and t19.a != 1)
  or t13.a = 4 and (t9.a != 1  and t11.a != 1  and t13.a != 1 and t15.a = 1 and t17.a != 1 and t19.a != 1)
  or t13.a = 5 and (t9.a != 1  and t11.a != 1  and t13.a != 1 and t15.a != 1 and t17.a = 1 )
)
) /* 13 */
and
(
t14.a = (case when t1.a = 4 then 1 else 0 end
+ case when t2.a = 4 then 1 else 0 end
+ case when t3.a = 4 then 1 else 0 end
+ case when t4.a = 4 then 1 else 0 end
+ case when t5.a = 4 then 1 else 0 end
+ case when t6.a = 4 then 1 else 0 end
+ case when t7.a = 4 then 1 else 0 end
+ case when t8.a = 4 then 1 else 0 end
+ case when t9.a = 4 then 1 else 0 end
+ case when t10.a = 4 then 1 else 0 end
+ case when t11.a = 4 then 1 else 0 end
+ case when t12.a = 4 then 1 else 0 end
+ case when t13.a = 4 then 1 else 0 end
+ case when t14.a = 4 then 1 else 0 end
+ case when t15.a = 4 then 1 else 0 end
+ case when t16.a = 4 then 1 else 0 end
+ case when t17.a = 4 then 1 else 0 end
+ case when t18.a = 4 then 1 else 0 end
+ case when t19.a = 4 then 1 else 0 end
+ case when t20.a = 4 then 1 else 0 end) - 5
) /* 14 */
and
(
t15.a = t12.a
) /* 15 */
and
(
    (t16.a = 1 and t10.a = 4)
or (t16.a = 2 and t10.a = 3)
or (t16.a = 3 and t10.a = 2)
or (t16.a = 4 and t10.a = 1)
or (t16.a = 5 and t10.a = 5)
) /* 16 */
and
(
   (t17.a = 1 and t6.a = 3)
or (t17.a = 2 and t6.a = 4)
or (t17.a = 3 and t6.a = 5)
or (t17.a = 4 and not t6.a in (3, 4, 5)) 
) /* 17 */
 
and
(
(t18.a = 1 and
((case when t1.a = 1 then 1 else 0 end
+ case when t2.a = 1 then 1 else 0 end
+ case when t3.a = 1 then 1 else 0 end
+ case when t4.a = 1 then 1 else 0 end
+ case when t5.a = 1 then 1 else 0 end
+ case when t6.a = 1 then 1 else 0 end
+ case when t7.a = 1 then 1 else 0 end
+ case when t8.a = 1 then 1 else 0 end
+ case when t9.a = 1 then 1 else 0 end
+ case when t10.a = 1 then 1 else 0 end
+ case when t11.a = 1 then 1 else 0 end
+ case when t12.a = 1 then 1 else 0 end
+ case when t13.a = 1 then 1 else 0 end
+ case when t14.a = 1 then 1 else 0 end
+ case when t15.a = 1 then 1 else 0 end
+ case when t16.a = 1 then 1 else 0 end
+ case when t17.a = 1 then 1 else 0 end
+ case when t18.a = 1 then 1 else 0 end
+ case when t19.a = 1 then 1 else 0 end
+ case when t20.a = 1 then 1 else 0 end) = 
 (case when t1.a = 2 then 1 else 0 end
+ case when t2.a = 2 then 1 else 0 end
+ case when t3.a = 2 then 1 else 0 end
+ case when t4.a = 2 then 1 else 0 end
+ case when t5.a = 2 then 1 else 0 end
+ case when t6.a = 2 then 1 else 0 end
+ case when t7.a = 2 then 1 else 0 end
+ case when t8.a = 2 then 1 else 0 end
+ case when t9.a = 2 then 1 else 0 end
+ case when t10.a = 2 then 1 else 0 end
+ case when t11.a = 2 then 1 else 0 end
+ case when t12.a = 2 then 1 else 0 end
+ case when t13.a = 2 then 1 else 0 end
+ case when t14.a = 2 then 1 else 0 end
+ case when t15.a = 2 then 1 else 0 end
+ case when t16.a = 2 then 1 else 0 end
+ case when t17.a = 2 then 1 else 0 end
+ case when t18.a = 2 then 1 else 0 end
+ case when t19.a = 2 then 1 else 0 end
+ case when t20.a = 2 then 1 else 0 end)))
or (t18.a = 2 and
((case when t1.a = 1 then 1 else 0 end
+ case when t2.a = 1 then 1 else 0 end
+ case when t3.a = 1 then 1 else 0 end
+ case when t4.a = 1 then 1 else 0 end
+ case when t5.a = 1 then 1 else 0 end
+ case when t6.a = 1 then 1 else 0 end
+ case when t7.a = 1 then 1 else 0 end
+ case when t8.a = 1 then 1 else 0 end
+ case when t9.a = 1 then 1 else 0 end
+ case when t10.a = 1 then 1 else 0 end
+ case when t11.a = 1 then 1 else 0 end
+ case when t12.a = 1 then 1 else 0 end
+ case when t13.a = 1 then 1 else 0 end
+ case when t14.a = 1 then 1 else 0 end
+ case when t15.a = 1 then 1 else 0 end
+ case when t16.a = 1 then 1 else 0 end
+ case when t17.a = 1 then 1 else 0 end
+ case when t18.a = 1 then 1 else 0 end
+ case when t19.a = 1 then 1 else 0 end
+ case when t20.a = 1 then 1 else 0 end) = 
 (case when t1.a = 3 then 1 else 0 end
+ case when t2.a = 3 then 1 else 0 end
+ case when t3.a = 3 then 1 else 0 end
+ case when t4.a = 3 then 1 else 0 end
+ case when t5.a = 3 then 1 else 0 end
+ case when t6.a = 3 then 1 else 0 end
+ case when t7.a = 3 then 1 else 0 end
+ case when t8.a = 3 then 1 else 0 end
+ case when t9.a = 3 then 1 else 0 end
+ case when t10.a = 3 then 1 else 0 end
+ case when t11.a = 3 then 1 else 0 end
+ case when t12.a = 3 then 1 else 0 end
+ case when t13.a = 3 then 1 else 0 end
+ case when t14.a = 3 then 1 else 0 end
+ case when t15.a = 3 then 1 else 0 end
+ case when t16.a = 3 then 1 else 0 end
+ case when t17.a = 3 then 1 else 0 end
+ case when t18.a = 3 then 1 else 0 end
+ case when t19.a = 3 then 1 else 0 end
+ case when t20.a = 3 then 1 else 0 end)))
or (t18.a = 3 and
((case when t1.a = 1 then 1 else 0 end
+ case when t2.a = 1 then 1 else 0 end
+ case when t3.a = 1 then 1 else 0 end
+ case when t4.a = 1 then 1 else 0 end
+ case when t5.a = 1 then 1 else 0 end
+ case when t6.a = 1 then 1 else 0 end
+ case when t7.a = 1 then 1 else 0 end
+ case when t8.a = 1 then 1 else 0 end
+ case when t9.a = 1 then 1 else 0 end
+ case when t10.a = 1 then 1 else 0 end
+ case when t11.a = 1 then 1 else 0 end
+ case when t12.a = 1 then 1 else 0 end
+ case when t13.a = 1 then 1 else 0 end
+ case when t14.a = 1 then 1 else 0 end
+ case when t15.a = 1 then 1 else 0 end
+ case when t16.a = 1 then 1 else 0 end
+ case when t17.a = 1 then 1 else 0 end
+ case when t18.a = 1 then 1 else 0 end
+ case when t19.a = 1 then 1 else 0 end
+ case when t20.a = 1 then 1 else 0 end) = 
 (case when t1.a = 4 then 1 else 0 end
+ case when t2.a = 4 then 1 else 0 end
+ case when t3.a = 4 then 1 else 0 end
+ case when t4.a = 4 then 1 else 0 end
+ case when t5.a = 4 then 1 else 0 end
+ case when t6.a = 4 then 1 else 0 end
+ case when t7.a = 4 then 1 else 0 end
+ case when t8.a = 4 then 1 else 0 end
+ case when t9.a = 4 then 1 else 0 end
+ case when t10.a = 4 then 1 else 0 end
+ case when t11.a = 4 then 1 else 0 end
+ case when t12.a = 4 then 1 else 0 end
+ case when t13.a = 4 then 1 else 0 end
+ case when t14.a = 4 then 1 else 0 end
+ case when t15.a = 4 then 1 else 0 end
+ case when t16.a = 4 then 1 else 0 end
+ case when t17.a = 4 then 1 else 0 end
+ case when t18.a = 4 then 1 else 0 end
+ case when t19.a = 4 then 1 else 0 end
+ case when t20.a = 4 then 1 else 0 end)))
or (t18.a = 4 and
((case when t1.a = 1 then 1 else 0 end
+ case when t2.a = 1 then 1 else 0 end
+ case when t3.a = 1 then 1 else 0 end
+ case when t4.a = 1 then 1 else 0 end
+ case when t5.a = 1 then 1 else 0 end
+ case when t6.a = 1 then 1 else 0 end
+ case when t7.a = 1 then 1 else 0 end
+ case when t8.a = 1 then 1 else 0 end
+ case when t9.a = 1 then 1 else 0 end
+ case when t10.a = 1 then 1 else 0 end
+ case when t11.a = 1 then 1 else 0 end
+ case when t12.a = 1 then 1 else 0 end
+ case when t13.a = 1 then 1 else 0 end
+ case when t14.a = 1 then 1 else 0 end
+ case when t15.a = 1 then 1 else 0 end
+ case when t16.a = 1 then 1 else 0 end
+ case when t17.a = 1 then 1 else 0 end
+ case when t18.a = 1 then 1 else 0 end
+ case when t19.a = 1 then 1 else 0 end
+ case when t20.a = 1 then 1 else 0 end) = 
 (case when t1.a = 5 then 1 else 0 end
+ case when t2.a = 5 then 1 else 0 end
+ case when t3.a = 5 then 1 else 0 end
+ case when t4.a = 5 then 1 else 0 end
+ case when t5.a = 5 then 1 else 0 end
+ case when t6.a = 5 then 1 else 0 end
+ case when t7.a = 5 then 1 else 0 end
+ case when t8.a = 5 then 1 else 0 end
+ case when t9.a = 5 then 1 else 0 end
+ case when t10.a = 5 then 1 else 0 end
+ case when t11.a = 5 then 1 else 0 end
+ case when t12.a = 5 then 1 else 0 end
+ case when t13.a = 5 then 1 else 0 end
+ case when t14.a = 5 then 1 else 0 end
+ case when t15.a = 5 then 1 else 0 end
+ case when t16.a = 5 then 1 else 0 end
+ case when t17.a = 5 then 1 else 0 end
+ case when t18.a = 5 then 1 else 0 end
+ case when t19.a = 5 then 1 else 0 end
+ case when t20.a = 5 then 1 else 0 end)))
) /* 18 */

Logical puzzles are not frequently being part of enterprise application, but I found it really assuring that SQL engine can work on my WHERE clauses with such effectivenes.