24点四则运算无解表

1、(1,1,1,1 )(1, 1, 1,2 ) ( 1, 1, 1,3 ) ( 1, 1, 1,4 ) ( 1, 1, 1,5(1, 1, 1,7 )(1, 1, 1,9 ) ( 1, 1, 1, 10 ) ( 1, 1,2, 2 ) ( 1, 1,2,3(1,1, 2, 5 )(1,1,3,3 )( 1, 1,4, 11 )(1, 1,4, 13 )(1,1,5,10 )(1,1,5,11 )( 1,1,5,12 ,)(1,1,5,13 )(1,1,6,10 )(1,1,6,11 )( 1, 1,6, 13)(1, 1,7,7 )(1, 1,7,9 )(1, 1, 7, 11 )( 1, 1,

2、7, 12 )(1,1,7,13 )(1, 1,&10 )() ( 1, 1,&12 :)(1, 1,&13 )(1,1,9,10 )(1,1,9,11 )( 1, 1,9, 12 )(1,1,10,10 )(1,2, 2, 2 )(1,2,2,3 )( 1,2,5,11 )(1,2,7,13 )(1,2,&12 )(1,2,9,9 )( 1,2,9, 10 )(1,2,10,10 )(1,3, 5, 5 )(1,3,7,11 )( 1,3, 10,13 )(1,3,11,13 )(1,4,7,10 )(1, 4, 8,10 ) ( 1,4, 9,9 )(1,4,10,13 )(1,4,11,

3、12 )(1,4,11,13 )( 1,4,12,13)(1,4,13,13(1,5, 5, 8 )(1,5,7,7 )( 1,5,11,13 )(1,5,12,13 )(1,6, 6, 7 )(1,6,7,7 )( 1,6,7,8 )(1,6,7,13 )(1,6, 10, 10 )(1,6,10,11 ) ( 1,6, 11, 11)(1,6,13,13(1,7, 7,8 )(1,7,7,13 )( 1,7,&13 )(1,7,10,10 )(1,7,11,11 )(1,7,11,12 )( 1,7, 11, 13)(1,&13 ；(1, & 9, 10 )(1, & 10, 10 ) (

4、 1, & 11, 11 )(1, & 12,13 )(1,9, 9,9 )(1,9,9, 10 )( 1,9,9, 11 )(1,9,9, 13 )(1,9, 10, 11 )(1,9,12, 13 ) ( 1,9, 13, 13 )(1, 10, 10, 10 )(1, 10, 10, 13)(1, 10, 11, 11 ) ( 1,10,11,13)(1,11,11,11 )(1, 13, 13, 13 )最小数为2 （46组）(2, 2, 2, 2 )(2,2,2,6 )( 2,2,5,13 )(2, 2, 7, 9 )(2,2,&11 )(2,2,&13 )( 2,2,9,9 )(2

5、,2,9,13 )(2, 3, 3, 4 )(2,3,9, 11 )( 2, 3, 10, 11 )(2,4,7,13 )(2, 4, 11, 13 )|( 2,4,12,13 )( 2,5,5,5)(2, 5, 5, 6 )(2, 5,9,9 )(2,5,9,13 )( 2,5,11,11 )(2,5,11,13 )(2, 6, 7, 7 )(2,6,9,13 )( 2, 6, 11, 11 )(2,6, 13, 13 )(2, 7, 7, 9 )(2,7,&10 )( 2,7,9,9 )(2,7,9,12 )(2, 7,11,11 )(2, 7, 11, 13 )( 2, 7, 13, 1

6、3)(2, & 11,1324点四则运算无解表（共458组）最小数为1（113组）)(1,1, 1,6 ) )(1, 1,2,4 )(1, 1,5,9 )(1, 1,6,7 )(1, 1,7,8 )(1,1, & 9 )(1, 1,9,9 ) (1,1,10,11 ) () (1,3,3, 13 ) (1,4,4,13 )(1,4,11,11 ) | ( 1,5,5,7 ) (1,5,13,13 ) (1,6,9, 11 ) | ( 1,7,7,7 )(1,7, 10, 11 )(1,&9,9 ) (1, & 13, 13 ) (1,9, 10, 10 ) (1, 10, 10, 11 )1,

7、 10, 13, 13)(2, 2, 7, 11 ) (2,2,10,12 )(2,4,9,11 )(2, 5, 7, 12 ) (2, 5, 13, 13 )(2, 7, 7, 7 ) :2,7,10,13 ) | ( 2, 9, 9, 9 )(2,9,9,10 ) ( 2, 9, 11, 12 ) ( 2,9,12,12 ) ( 2, 10, 10, 10)(2, 10, 12, 12 )(2, 10, 13, 13 )最小数为3 (47组)(3, 3, 3, 13 )( 3, 3, 4, 10(3, 3, & 11 ) (3,3, 10, 10(3, 3, 13, 13 )( 3,4,

8、6, 7)(3, 3, 5, 8)(3,3, 10, 11)(3,4,7,13)(3, 3, 5, 11 )(3,3, 10, 12)(3,4, & 8(3,4, 10, 11(3, 5, 5, 13(3,6,7,11(3, 7, 10, 12)()()()3, 4, 11, 11 ) ( 3,4, 13, 13 ) ( 3, 5, 5, 53,5,7,7 ) ( 3,5, &10 ) ( 3,5,9,113, 6, 8, 11 )( 3,6, 10, 13 )( 3, 7, 7, 113, 7,11, 13)(3,& 13) (3, 8,10, 13(3, 10,10,11)(3, 10,1

9、0, 13)(3, 10,12,13)(3, 10,13, 13)3, 11, 12, 13 )(3,11,13,13 )( 3, 13,13,:(3, 10, 10, 10(3, 10, 12, 12(3,11,11,13 )最小数为4 (48组)(4,4,4,13 ) ( 4, 4, 5, 9 ) ( 4, 4, 6, 6 ) ( 4, 4, 6, 7 ) ( 4,4,(4,4,9,10 ) ( 4,4,9, 13 )( 4,4,10,11 ) ( 4,4,11,11(4,5,5,11)( 4,5,5, 12 )(4,5,5, 13 )(4,5,9,11(4,6,6, 13)( 4,6,7

10、,11 )(4,6,7, 13 )(4,6,&11(4, 6, 10, 13 )( 4,6, 11, 13 )( 4, 7, 7, 9 )( 4, 7, 7, 10(4, 7, 7, 13 )( 4,7,10,13 )( 4, & 10,13 )( 4, 9, 9, 9(4,9,9,13 ) ( 4,9, 10, 10 ) ( 4,9, 11, 13 ) ( 4,9,12,13 (4, 10, 10, 10)(4, 10, 10, 13)(4,10,11,11)(4, 11, 11, 11)(4,11,11,12)(4,11,11,13)(4, 11, 13, 13 )(4, 12, 12,

11、13 ) ( 4, 12,13,13 ) ( 4, 13,13,最小数为5 (59组)(5, 5, 5, 7 )(5, 5, 6, 9 )(5, 5, 7, 12 )(5,6,6,11 )(5, 7, 7, 7 )(5, 7, 8, 12 )()(5, & 10, 13 )(5,9,9,10 )(5, 9, 13, 13 )(5, 11, 11, 11(5, 5, 5, 8 )(5, 5, 6, 10 ) (5, 5, 7, 13 ) (5,6,6,13 )(5, 7, 7, 8 )(5, 7, 8,13 )(5,&12 )(5,5,5,10 )(5,5,6,12 )(5,5,9,12 )(5

12、, 6, 7, 10 )(5, 7, 7, 12 )(5, 7, 9, 9 )(5, & 9, 9 )(5,5,5,11(5, 5, 6, 13(5, 5, 9, 13(5, 6, 7, 11(5, 7, 7, 13(5,7,11,12(5, & 9, 10(5, & 11, 11 )( 5,& 12, 13 ) ( 5, & 13,(5,9,9,13 )( 5,9,10,12 ) ( 5,9,11,11(5, 10, 10, 10 ) ( 5, 10, 11, 12 ) (5, 10, 11, 1)(5,11,11,12)(5,11,11,13)(3, 3, 7, 10 ) )(3, 3,

13、11, 11 ) )(3,4,9,10 )(3, 5, 5, 10 )(3,5, 11, 13 )(3,7,&10 ) )(3, & 11,13 ) (3, 10, 11, 11 ) (3, 11, 11, 11 ) .3 )Ml ) ( 4, 4, 9, 9 )(4,4,13,13 ) )(4, 6, 6, 11 ) )(4,6,9, 11 ) )(4, 7, 7, 12 ) )(4,9,9, 11 ) )(4,9,13,13 ) (4, 10, 13, 13 ) (4, 11, 12, 12 ) 13 )(5,5,5,13 )(5, 5, 7, 9 )(5,5,10,12 )(5,6,&1

14、1 )(5,7,&11 ) )(5,7,12,13 ) )(5, & 10, 10 ) 3 ) ( 5, 9, 9, 9 ) )(5,9,11,12 ) )(5, 10, 12, 12 ) (5, 11, 12, 13)(5, 11, 13, 13)(5,12,12,12)(5,12,12,13)(5, 13, 13, 13 )最小数为6 (40组)(6, 6, 6, 7 )(6, 6, 10, 10 )(6, 7, 7, 8 )(6, 7, 8, 13 )(6, 7, 13, 13 )(6,9,9,13 )(6, 10, 10, 11(6, 10, 13, 13(6, 13, 13, 13

15、)最小数为7 (48组)(7, 7, 7, 7 )()()()(6, 6, 6,13 ) ( 6, 6, 7, 7 ) ( 6, 6, 7, 8 ) ( 6, 6, (6, 6, 10, 11 ) ( 6,6, 11, 11 ) ( 6,6, 13,: (6, 7, 7, 9 )( 6, 7, 7, 12 )( 6, 7, 7, 13(6, 7, 9, 10 ) ( 6,7,9,11 ) ( 6, 7,9, 13(6, & 13 )( 6,& 10, 10 )( 6, & 12, 1(6, 9, 10, 10 ) ( 6,9, 10, 13 ) ( 6,9, 11, 11(6, 10, 10,

16、 12 )(6,11,11,11 )(6, 10, 11, 11 )6, 11, 11, 13)(5, 12, 13, 13)7, 13 ) ( 6, 6, 9, 9 ) 3 ) ( 6, 7, 7, 7 )(6,7, & 8 )(6,7,10,11 )3 ) ( 6, 9, 9, 9 )(6,9,13,13 )(6, 10, 11, 13 )(6, 11, 13, 13 )(7, 7, 7, 13(7, 7, 8,13(7, 7, 10, 10(7,&8 )(7, 8, 13, 13(7,9, 10, 107, 7, 7, 87, 7, 8,87, 7, 9, 97, 7, 10, 11(7

17、, & 9, 9 )(7, 9, 9, 9)(7, 9,10,13)(7, 7, 7, 9 ,7, 7, 8, 97, 7, 9,117, 7, 10, 127, & 9, 11 )(7, 9, 9,10(7, 9, 11, 13)(7,7, 7, 10)(7,7, 8,10)(7, 7, 9, 12! ) ( 7,7,11,11(7, & 10, 12)(7,9,9,11)(7,9, 12, 13)(7, 10, 10, 13(7, 11, 11, 11(7, 11, 12, 13(7, 13, 13, 13 )最小数为8 (29组)(8, 8, 8, 8 ) ( &9 ) (& 8, 9,

18、9 ) ( & & 9, 10 ) (& 10, 11 ) ( & 11, 11 ) ( & 13, 13 ) (& 9, 9,9 (& 9, 9, 11 ) (& 9,9, 13 )( 8, 9, 10, 10(& 10, 10,10(& 10, 11, 13(& 11, 12, 13(& 12, 13, 13 )(7,10,11,11)(7,11,11,12)(7,11,13,13)(7,10,11,12)(7,11,11,13)(7, 12, 12, 12)(7, 7, 7, 11 )(7,7,&12 )(7, 7, 9,13 )(7,7,13,13 )(7,8, 11, 11 )(7,9,9,12 )(7, 10, 10, 10 )(7, 10, 13, 13)(7,11,12,12)(7, 12, 13, 13)(& 10,10,11)(& 11,11,11)(& 11,13,13(& 13,