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Four fours

0     44 - 44                         26   4! +    4 -4+4
1     44 ÷44                          27                4
2      4 4                                 4! + 4 +
          +                                             4
       4 4                            28   4! + 4 - 4 +4
3     (4+4+4)÷4                       29              4
4                                          4! + 4 +
         4 + 4 + 4 -4                                 4
5                  4                  30     4 + 4 + 4! + 4
         4 +4-
                   4                  31          4
6        4 +4-4+4                          4! + . - 4 =
                                                 ⋅4
7                4
      4+4+                                 ((4 + 4 )! + 4!)/ 4!
                 4
                                      32   (4 × 4) + (4 × 4)
8        4+ 4+ 4+ 4                   33   4! + (4!/ 4) + 4
9                4                    34
      4+4+                                 4! + 4 + 4 + 4
                 4                    35   4! + 44/4
10      4 4                           36
         . +    = (44-4)/4                 (4 + 4 ) × (4 + 4 )
       ⋅4 4                           37   4! + (4! + 4 )/ 4
11      4 4                           38   44 - (4! / 4)
           + = 44/ ( 4 + 4 )
       ⋅4 4                           39   (4 +   4)÷
                                                           .

12                                                          ⋅4
         4× 4× 4+4
                                      40                      4
13     44                                  ( 4 + 4)×
           + 4                                               ⋅4
        4
                                      41   (4 × 4 + ⋅ 4 ) ÷ ⋅ 4
14    4+4+4+ 4                        42   (4! + 4!) - ( 4 + 4)
15              4
      4+4-                            43         4
                4                          44 -
                                                 4
16    4+4+4+4
                                      44   44 - 4 + 4
17               4
      4×4+                            45          4
                 4                         44 +
                                                  4
18    (4! + 4! + 4!) /4
                                      46   4! + 4 + 4! - 4
19      4      4
            + . = 4! - 4 – (4/ 4)     47              4
       ⋅4 ⋅4                               4! + 4! -
                                                      4
20      4      4                      48   4! + 4! - 4 + 4
            +     = 4! - 4 + (4/ 4)
       ⋅4 ⋅4                          49               4
21               4                         4! + 4! +
      4! - 4 +                                         4
                 4                    50   4! + 4! + 4 - 4
22    ( 4 + 4) + (4 × 4)              51   (4! - 4 + ⋅ 4 ) ÷ ⋅ 4
23                  4                 52   4! + 4! + 4 + 4
      4! - 4 +
                    4                 53          4
24    ( 4 + 4) ( 4 + 4 )                   44 + .
25                                               ⋅4
        4
         . + (4 × 4) = 4! + 4
                              (4-4)   54   4! + 4! + 4 + 4
       ⋅4                             55   (4! - 4 + 4 )/.4
56   4! + 4! + 4 - 4                84    44 ×   4 -4
57                 4                85           4
     (4! + 4!) + .                        4
                                            +4
                  ⋅4                       .
58               4                        ⋅4
     4! + 4! +                      86
                ⋅4                        44 × 4 - 4
     ((4!+4) 4 )+               4   87                 4
                                          (4! × 4) -
59              4                                     ⋅4
     4! ÷ ⋅ 4 -                     88    (4! × 4) - (4 + 4)
                4
60   4×4×4-4                        89    ((4! + 4 ) ÷ ⋅ 4 ) + 4!)
61                                  90    (4! × 4) - (4 + 4 )
62   (44 ÷ 4) - 4                   91    4 × 4! - ( 4 / ⋅ 4 )
63   (44 - 4) ÷ 4                   92    44 × 4 + 4
64   (4 + 4) × (4 + 4)              93                  4
65   (44 + 4) ÷ 4                         (4! × 4) -     .
66   44 + 4! - 4                                        ⋅4
67    (4! + 4 ) ÷ ⋅ 4 + 4           94    (4! × 4) - 4 - 4
68   4! + 4! + 4! - 4               95    (4! × 4) - (4 ÷ 4)
69   (4! + 4 - ⋅ 4 ) ÷ ⋅ 4          96    (4! × 4) + (4 - 4)
70   4! + 4! + 4! - 4               97                4
                                          (4! × 4) +
71   (4! + 4.4) ÷ ⋅ 4                                 4
72               4                  98    (4! × 4) + (4 - 4 )
     (4 × 4) × .                    99
                ⋅4                                       4
                                          (4! × 4) +      .
73                  4                                   ⋅4
             4! +
           4         .
                                    100
                   ⋅4                     (4! × 4) + 4 + 4
74   4! + 4! + 4! + 4
75   (4! + 4 + 4 ) ÷ ⋅ 4
76   4! + 4! + 4! + 4
77   4
               4

       -4
      .
     ⋅4
78   4 (4! - 4) -           4
79   4
               4

       -              4
      .
     ⋅4
80                      4
     (4 + 4) ×
                       ⋅4
81    4        4
       .   ×       .
     ⋅4 ⋅4
82   4 (4! -4) +            4
83   4
               4

       +              4
      .
     ⋅4
Using one 4
 4 =2              4
                   .   =9
                  ⋅4
4
                   4
4! = 24              = 10
                  ⋅4

Using two 4s      4 × 4 = 16

4 -4 = 0          4! - 4 = 20

4                 ( 4 +     4 )! = 24
  =1
4
                  4! + 4 = 28
4-       4 =2
                  4! ÷ ⋅ 4 = 60
     4
     .   =3            4 4! = 64
    ⋅4
                  44
    4 +    4 =4   4! + 4! = 48
                  4! × 4 = 96
4+       4 =6     44 = 256
                  (4+ 4 )! = 720
4+4=8

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Four Fours Solutions

  • 1. Four fours 0 44 - 44 26 4! + 4 -4+4 1 44 ÷44 27 4 2 4 4 4! + 4 + + 4 4 4 28 4! + 4 - 4 +4 3 (4+4+4)÷4 29 4 4 4! + 4 + 4 + 4 + 4 -4 4 5 4 30 4 + 4 + 4! + 4 4 +4- 4 31 4 6 4 +4-4+4 4! + . - 4 = ⋅4 7 4 4+4+ ((4 + 4 )! + 4!)/ 4! 4 32 (4 × 4) + (4 × 4) 8 4+ 4+ 4+ 4 33 4! + (4!/ 4) + 4 9 4 34 4+4+ 4! + 4 + 4 + 4 4 35 4! + 44/4 10 4 4 36 . + = (44-4)/4 (4 + 4 ) × (4 + 4 ) ⋅4 4 37 4! + (4! + 4 )/ 4 11 4 4 38 44 - (4! / 4) + = 44/ ( 4 + 4 ) ⋅4 4 39 (4 + 4)÷ . 12 ⋅4 4× 4× 4+4 40 4 13 44 ( 4 + 4)× + 4 ⋅4 4 41 (4 × 4 + ⋅ 4 ) ÷ ⋅ 4 14 4+4+4+ 4 42 (4! + 4!) - ( 4 + 4) 15 4 4+4- 43 4 4 44 - 4 16 4+4+4+4 44 44 - 4 + 4 17 4 4×4+ 45 4 4 44 + 4 18 (4! + 4! + 4!) /4 46 4! + 4 + 4! - 4 19 4 4 + . = 4! - 4 – (4/ 4) 47 4 ⋅4 ⋅4 4! + 4! - 4 20 4 4 48 4! + 4! - 4 + 4 + = 4! - 4 + (4/ 4) ⋅4 ⋅4 49 4 21 4 4! + 4! + 4! - 4 + 4 4 50 4! + 4! + 4 - 4 22 ( 4 + 4) + (4 × 4) 51 (4! - 4 + ⋅ 4 ) ÷ ⋅ 4 23 4 52 4! + 4! + 4 + 4 4! - 4 + 4 53 4 24 ( 4 + 4) ( 4 + 4 ) 44 + . 25 ⋅4 4 . + (4 × 4) = 4! + 4 (4-4) 54 4! + 4! + 4 + 4 ⋅4 55 (4! - 4 + 4 )/.4
  • 2. 56 4! + 4! + 4 - 4 84 44 × 4 -4 57 4 85 4 (4! + 4!) + . 4   +4 ⋅4  . 58 4 ⋅4 4! + 4! + 86 ⋅4 44 × 4 - 4 ((4!+4) 4 )+ 4 87 4 (4! × 4) - 59 4 ⋅4 4! ÷ ⋅ 4 - 88 (4! × 4) - (4 + 4) 4 60 4×4×4-4 89 ((4! + 4 ) ÷ ⋅ 4 ) + 4!) 61 90 (4! × 4) - (4 + 4 ) 62 (44 ÷ 4) - 4 91 4 × 4! - ( 4 / ⋅ 4 ) 63 (44 - 4) ÷ 4 92 44 × 4 + 4 64 (4 + 4) × (4 + 4) 93 4 65 (44 + 4) ÷ 4 (4! × 4) - . 66 44 + 4! - 4 ⋅4 67 (4! + 4 ) ÷ ⋅ 4 + 4 94 (4! × 4) - 4 - 4 68 4! + 4! + 4! - 4 95 (4! × 4) - (4 ÷ 4) 69 (4! + 4 - ⋅ 4 ) ÷ ⋅ 4 96 (4! × 4) + (4 - 4) 70 4! + 4! + 4! - 4 97 4 (4! × 4) + 71 (4! + 4.4) ÷ ⋅ 4 4 72 4 98 (4! × 4) + (4 - 4 ) (4 × 4) × . 99 ⋅4 4 (4! × 4) + . 73 4 ⋅4 4! + 4 . 100 ⋅4 (4! × 4) + 4 + 4 74 4! + 4! + 4! + 4 75 (4! + 4 + 4 ) ÷ ⋅ 4 76 4! + 4! + 4! + 4 77 4 4   -4  . ⋅4 78 4 (4! - 4) - 4 79 4 4   - 4  . ⋅4 80 4 (4 + 4) × ⋅4 81 4 4 . × . ⋅4 ⋅4 82 4 (4! -4) + 4 83 4 4   + 4  . ⋅4
  • 3. Using one 4 4 =2 4 . =9 ⋅4 4 4 4! = 24 = 10 ⋅4 Using two 4s 4 × 4 = 16 4 -4 = 0 4! - 4 = 20 4 ( 4 + 4 )! = 24 =1 4 4! + 4 = 28 4- 4 =2 4! ÷ ⋅ 4 = 60 4 . =3 4 4! = 64 ⋅4 44 4 + 4 =4 4! + 4! = 48 4! × 4 = 96 4+ 4 =6 44 = 256 (4+ 4 )! = 720 4+4=8