-- more about the SQL:
-- https://www.orczhou.com/index.php/2024/03/a-sql-for-24-point-game/
 select id,t.c1,t.c2,t.c3,t.c4,
    (
    select result_expr
    FROM
    (
        select

        @if_found := false,
        @r_expr := 'failed',

        t_each_row.id,c1,c2,c3,c4, op_1st,op_2nd,op_3rd,
        @c_1 := case full_order.seq_num_1 
            when 1 then c1 
            when 2 then c2 
            when 3 then c3 
            when 4 then c4 
        END as c_1,
        @c_2 := case full_order.seq_num_2
            when 1 then c1 
            when 2 then c2 
            when 3 then c3 
            when 4 then c4 
        END as c_2,
        @c_3 := case full_order.seq_num_3
            when 1 then c1 
            when 2 then c2 
            when 3 then c3 
            when 4 then c4 
        END as c_3,
        @c_4 := case full_order.seq_num_4
            when 1 then c1 
            when 2 then c2 
            when 3 then c3 
            when 4 then c4 
        END as c_4,
--    , @c_1,@c_2,@c_3,@c_4,
    
    
        /* total 5 trees */   
        /*left most tree*/
        /* ((@c_1 op_1 @c_2) op_2 @c_3) op_3 @c_4  */
        @lt_1 := case op_1st 
            when '*' then @c_1 * @c_2
            when '+' then @c_1 + @c_2
            when '-' then @c_1 - @c_2
            when '/' then @c_1 / @c_2
        END as lt_1,
        
        @lt_2 := case op_2nd 
            when '*' then @lt_1 * @c_3
            when '+' then @lt_1 + @c_3
            when '-' then @lt_1 - @c_3
            when '/' then @lt_1 / @c_3
        END as lt_2,
        
        @lt_3 := case op_3rd 
            when '*' then @lt_2 * @c_4
            when '+' then @lt_2 + @c_4
            when '-' then @lt_2 - @c_4
            when '/' then @lt_2 / @c_4
        END as lt_3,
        
        @lt_expr := concat("((", @c_1 ,op_1st,@c_2 ,")",op_2nd,@c_3,")",op_3rd,@c_4),
        if(@lt_3 between 24-0.0001 and 24+0.0001, @if_found := true, 0),
        if(@lt_3 between 24-0.0001 and 24+0.0001, @r_expr := @lt_expr, 0),
        
        /* bushy tree 00 */
        /* (c1 op_1st c2) op_2nd (c3 op_3rd c4)  */
        if(
            @if_found = false,
            @bt_1 := case op_1st
                when '*' then @c_1 * @c_2
                when '+' then @c_1 + @c_2
                when '-' then @c_1 - @c_2
                when '/' then @c_1 / @c_2
            END,
            0
            ) as bt_1,
        
        if(
            @if_found = false,
            @bt_2 := case op_3rd
                when '*' then @c_3 * @c_4
                when '+' then @c_3 + @c_4
                when '-' then @c_3 - @c_4
                when '/' then @c_3 / @c_4
            END,
            0
            ) as bt_2,
    
        if(
            @if_found = false,
            @bt_3 := case op_2nd
                /* '+' & '*' there is always a equel tree   */
                when '*' then @bt_1 * @bt_2
                when '+' then @bt_1 + @bt_2
                when '-' then @bt_1 - @bt_2
                when '/' then @bt_1 / @bt_2
            END,
            0
            ) as bt_3,
       
        
        @bt_expr := concat("(",@c_1,op_1st,@c_2,")",op_2nd,"(",@c_3,op_3rd,@c_4,")"),
        if(@bt_3 between 24-0.0001 and 24+0.0001, @if_found := true , 0),
        if(@bt_3 between 24-0.0001 and 24+0.0001, @r_expr := @bt_expr, 0),
   
 
        /*right most tree*/
        /* c1 op_1 (c2 op_2 (c3 op_3 c4))  */
        if(
            @if_found = false,
            @rt_1 := case op_3rd 
                when '*' then @c_3 * @c_4
                when '+' then @c_3 + @c_4
                when '-' then @c_3 - @c_4
                when '/' then @c_3 / @c_4
            END,
            0
            ) as rt_1,
    
        
        if(
            @if_found = false,
            @rt_2 := case op_2nd 
                when '*' then @c_2 * @rt_1  
                when '+' then @c_2 + @rt_1  
                when '-' then @c_2 - @rt_1  
                when '/' then @c_2 / @rt_1  
            END,
            0
            ) as rt_2,
        
        if(
            @if_found = false,
            @rt_3 := case op_1st
                when '*' then @c_1 * @rt_2
                when '+' then @c_1 + @rt_2
                when '-' then @c_1 - @rt_2
                when '/' then @c_1 / @rt_2
            END,
            0
            ) as rt_3,
    
        
        @rt_expr := concat(@c_1, op_1st, "(", @c_2 ,op_2nd, "(",@c_3, op_3rd, @c_4,")",")"),
        if(@rt_3 between 24-0.0001 and 24+0.0001, @if_found := true, 0),
        if(@rt_3 between 24-0.0001 and 24+0.0001, @r_expr := @rt_expr, 0),
    
        /* bushy tree 01  */
        /* (c2 op2 (c3 op3 c4)) op1 c1  */
        if(
            @if_found = false,
            @bt01_1 := case op_3rd
                when '*' then @c_3 * @c_4
                when '+' then @c_3 + @c_4
                when '-' then @c_3 - @c_4
                when '/' then @c_3 / @c_4
            END,
            0
            ) as bt01_1,
        
        if(
            @if_found = false,
            @bt01_2 := case op_2nd
                when '*' then @c_2 * @bt01_1
                when '+' then @c_2 + @bt01_1
                when '-' then @c_2 - @bt01_1
                when '/' then @c_2 / @bt01_1
            END,
            0
            ) as bt01_2,
        
        if(
            @if_found = false,
            @bt01_3 := case op_1st
                /* '+' & '*' there is always a equel tree   */
                when '*' then @bt01_2 * @c_1
                when '+' then @bt01_2 + @c_1
                when '-' then @bt01_2 - @c_1
                when '/' then @bt01_2 / @c_1
            END,
            0
            ) as bt01_3,
    
        @bt01_expr := concat("(",@c_2, op_2nd , "(" ,@c_3, op_3rd, @c_4, "))", op_1st, @c_1 ),
        if(@bt01_3 between 24-0.0001 and 24+0.0001 , @if_found := true , 0),
        if(@bt01_3 between 24-0.0001 and 24+0.0001 , @r_expr := @bt01_expr, 0),
    
        /* bushy tree 02  */
        /* c1 op1 ((c3 op3 c4) op2 c2)  */
        /* @c_1 op_1st (( @c_3 op_3rd  @c_4) op_2nd @c_2 ) */
        if(
            @if_found = false,
            @bt02_1 := case op_3rd
                when '*' then @c_3 * @c_4
                when '+' then @c_3 + @c_4
                when '-' then @c_3 - @c_4
                when '/' then @c_3 / @c_4
            END,
            0
            ) as bt02_1,
        
        if(
            @if_found = false,
            @bt02_2 := case op_2nd
                when '*' then @bt02_1 * @c_2
                when '+' then @bt02_1 + @c_2
                when '-' then @bt02_1 - @c_2
                when '/' then @bt02_1 / @c_2
            END,
            0
            ) as bt02_2,
        
        if(
            @if_found = false,
            @bt02_3 := case op_1st
                /* '+' & '*' there is always a equel tree   */
                when '*' then @c_1 * @bt02_2
                when '+' then @c_1 + @bt02_2
                when '-' then @c_1 - @bt02_2
                when '/' then @c_1 / @bt02_2
            END,
            0
            ) as bt02_3,
       
        @bt02_expr := concat( @c_1, op_1st, "((", @c_3, op_3rd,  @c_4,")", op_2nd, @c_2, ")"),
        if(@bt02_3 between 24-0.0001 and 24+0.0001 , @if_found := true , 0),
        if(@bt02_3 between 24-0.0001 and 24+0.0001 , @r_expr := @bt02_expr, 0),
      
      if(@if_found , @r_expr , "false") as result_expr,
      
      @if_found as if_found
      
      from 
            (select t.id,t.c1,t.c2,t.c3,t.c4) as 
--          (select 9 as id,9 as c1,3 as c2,1 as c3,10 as c4, @if_found := false) as 
          t_each_row , 
          
  
          (
          WITH RECURSIVE 
          seq (n) as (
          SELECT 1
          UNION ALL
          SELECT n + 1 FROM seq WHERE n <= 3
          )
          select 
              seq_1.n as seq_num_1,
              seq_2.n as seq_num_2,
              seq_3.n as seq_num_3,
              seq_4.n as seq_num_4
          from 
              seq as seq_1,
              seq as seq_2,
              seq as seq_3,
              seq as seq_4
          WHERE pow(2,seq_1.n-1)+pow(2,seq_2.n-1)+pow(2,seq_3.n-1)+pow(2,seq_4.n-1) = 15
          ) full_order
          ,
          (
          WITH
          op_list (op) as (
          SELECT '*'
          UNION
          SELECT '+'
          UNION
          SELECT '-'
          UNION
          SELECT '/'
          )
          SELECT op_1.op as op_1st,op_2.op as op_2nd,op_3.op as op_3rd FROM op_list as op_1,op_list as op_2,op_list as op_3
          ) full_op
      ) mid_result 
       WHERE
           result_expr != "false"
       LIMIT 1
   ) mid_result_01 
 from cards as t