The Four Fours

I've seen it as 1-100.

Hi Mark ..

When I last saw it was in 1965 and I don't remember what the range was .. 1 - 100 works for me ...

You should tell us what operators are allowed.

I think you need Factorial (!) and sqrt and perhaps the decimal point.

Whim

Yes, factorial and decimal points are allowed, but to do square root you must use some 4's ...

2 = 4 ^ 4/(4+4)

can't we use square root like this?

2 = (4 + sqrt(4*4))/4




1 = 44/44
2 = (44+4)/4!
3 = (4+4+4)/4
4 = (-44)+4!+4!
5 = (44-4!)/4
6 = (4+4)/4+4
7 = 44/4-4
8 = (44-4!)*.4
9 = 4+4+4/4
10 = (44-4)/4
11 = 4/4+4/.4
12 = (44+4)/4
13 = 44/(-4)+4!
14 = 4*(4-.4)-.4
15 = 44/4+4
16 = (44-4)*.4
17 = (44+4!)/4
18 = 44*.4+.4
19 = (4+4-.4)/.4
20 = (4/4+4)*4
21 = 4/4-4+4!
22 = (4+4)/((-4))+4!
23 = (4-4*4!)/((-4))
24 = 44+4-4!
25 = ((4-4)*4)!+4!
26 = 4*4+4/.4
27 = 4-4/4+4!
28 = 44-4*4
29 = 4/4+4+4!
30 = ((4/4+4)!)/4
31 = (4+4!)/4+4!
32 = 4*4+4*4
33 = (4-.4)/.4+4!
34 = 44-4/.4
35 = 44/4+4!
36 = 44-(4+4)
37 = (.4+4!)/.4-4!
38 = 44-4!/4
39 = (4*4-.4)/.4
40 = 4*4*4-4!
41 = (4*4+.4)/.4
42 = 4!/(-4)+4!+4!
43 = 44-4/4
44 = 44+4-4
45 = 44+4/4
46 = (4+4!)/.4-4!
47 = 4/(-4)+4!+4!
48 = (4+4+4)*4
49 = 4/4+4!+4!
50 = 44+4!/4
51 = (.4-4+4!)/.4
52 = 44+4+4
53 = ?

53 = (4!+4!)+(sqrt(4)/.4)

If sqrt is allowed

Great !!! Very clever !!! As I remember from when I first heard the problem (many years ago) sqrt was not allowed, just + - * / ! and . ............ you could use repeating decimals, such as .4...... = .4444444444444 etc

53 = 44+4/.4...
54 = 44+4/.4
55 = 44/(.4+.4 )
56 = 4*(4+4/.4)
57 = (.4+ 4!)/.4-4
58 = (4^4-4!)/4
59 = 4/(-4)+4!/.4
60 = 44+4*4
61 = 4/4+4!/.4
62 = (.4+.4+4!)/.4
63 = (4^4 -4)/4
64 = 44-4+4!
65 = (4^4+4 )/4
66 = (4+4!)/.4-4
67 = 4+(4+4!)/.4...
68 = 4*4*4+4
69 = (4-.4+4!)/.4
70 = (4^4+4!)/4
71 = (4+.4+4!)/.4
72 = 44+4+4!
73 = ?
74 = 4+(4+4!)/.4
75 = ((4!/4)!)/(.4*4!)
76 = 4*4 +4!/.4
77 = (4!-.4...)/.4r+4!
78 = 4!+4!/.44...
79 = (.4...+4!)/.4...+4!
80 = 4*(44-4!)
81 = (4- 4/4)^4
82 = 4+4!/.4...+4!
83 = (4!-.4)/.4+4!
84 = 4-4*(4-4!)
85 = (4 /.4+4!)/.4
86 = 44/.4-4!
87 = 4*4!-4/.4...
88 = 44+44
89 = ?
90 = ((4/.4)!)/((4+4)!)
91 = ?
92 = 44+4!+4!
93 = ?
94 = 4*(4!-.4)-.4
95 = 4/(-4)+4*4!
96 = ((4+ 4-4)!)*4
97 = 4/4+4*4!
98 = 4*(.4+4!)+.4
99 = 44 /.44...
100 = 44/.44



whim

You're more than whimsical, you're very clever.

I was never able to get that far ...

Thanks for the response ...

√= sqrt.
4^0=1
.............................................................................................................................
73=(4^0+√4)x4!+4^0
89=((√4+4!)/.4)+4!
91=4x4!-(√4/.4)

That answers your questions, whimsical

oh and sqrt is allowed
.4...=.44444444444444444444etc.

93=4!(4)-(√4/√.4...)