Dr. Ecco Solution
Solution to "The Luck of the 4," DDJ, January 2005.
Here are Tyler's expressions for 11-40. Twenty of these numbers required only three 4s. I'll report your solutions to the open problems in a future column.
11=44/4
12=4*sqrt(4/.4R)
13=(4/.4R)+4
14=4/.4+4
15=(4/(0.4*sqrt(.4R)))=4/(0.4*(2/3))=(3/2)*10
16=4*4
17=4*4+4/4
18=4*4+sqrt(4)
19=4!-sqrt(4)/0.4
20 =4*4+4
21 =4!-sqrt(4/.4R)
22 =4!-sqrt(4)
23 = 4!-4/4
24 = 4!
25 = 4!+4/4
26 = 4!+sqrt(4)
27 = 4!+sqrt(4/.4R)
28 = 4!+4
29 = 4!+sqrt(4)/0.4
30 = 4!+4+sqrt(4)
31 = 4+4!+sqrt(4/.4R)
32 = 4!+4+4
33 = 4!+4/.4R
34 = 4!+4/.4
35 = 4!+sqrt(4)+4/.4R
36 = 4!+sqrt(4)+4/.4
37 = 4!+4+4/.4R
38 = 4!+4+4/.4
39 = 44-sqrt(4)/0.4
40 = 4*(4/.4)
