(4+4.4 -4)
Using Four Fours How Can I Get 3, 4, 6, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25?
(4!+4-sqrt(4))/sqrt(4)
Using only addition, subtraction, multiplication, and division, these are the numbers you can build from four 4s.
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 16, 17, 20, 24, 28, 32, 36, 48, 60, 64, 68, 80, 128, 256
Several of the numbers on your list cannot be made using only the listed operations. Adding square root to the allowed operations adds a few more.
1 = 4/4+4-4
2 = 4 - (4+4)/4
3 = (4+4+4)/4
4 = 4 + 4*(4-4)
5 = (4+4*4)/4
6 = 4 + (4+4)/4
7 = 4+4 - 4/4
8 = (4+4)*4/4
9 = 4+4 + 4/4
12 = 4*(4 - 4/4)
15 = 4*4 - 4/4
16 = 4*4*4/4
17 = 4*4 + 4/4
20 = 4*(4+4/4)
24 = 4*4 + 4+4
28 = 4(4+4) - 4
32 = 4*4 + 4*4
36 = 4(4+4) + 4
48 = 4(4+4+4)
60 = 4*4*4 - 4
64 = (4+4)(4+4)
68 = 4*4*4 + 4
80 = 4(4+ 4*4)
128 = 4*4*(4+4)
256 = 4*4*4*4
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 16, 17, 20, 24, 28, 32, 36, 48, 60, 64, 68, 80, 128, 256
Several of the numbers on your list cannot be made using only the listed operations. Adding square root to the allowed operations adds a few more.
1 = 4/4+4-4
2 = 4 - (4+4)/4
3 = (4+4+4)/4
4 = 4 + 4*(4-4)
5 = (4+4*4)/4
6 = 4 + (4+4)/4
7 = 4+4 - 4/4
8 = (4+4)*4/4
9 = 4+4 + 4/4
12 = 4*(4 - 4/4)
15 = 4*4 - 4/4
16 = 4*4*4/4
17 = 4*4 + 4/4
20 = 4*(4+4/4)
24 = 4*4 + 4+4
28 = 4(4+4) - 4
32 = 4*4 + 4*4
36 = 4(4+4) + 4
48 = 4(4+4+4)
60 = 4*4*4 - 4
64 = (4+4)(4+4)
68 = 4*4*4 + 4
80 = 4(4+ 4*4)
128 = 4*4*(4+4)
256 = 4*4*4*4