ANSWERS to Sunny's Four 4's Challenge

Here are all the solutions to Sunny's Four 4's Challenge

If you find any errors, please let us know!

HINTS

^= power
Therefore 4^SQRT4 = 42=16

! = factorial
Therefore 4!= 4x3x2x1.

!! = double factorial
With an even number such as 4, you just multiply the even numbers, so
4!! = 4x2 =8 or 6!! = 6x4x2 = 48
or 8!! = 8x6x4x2=384.
With an odd number such as 7 you just multiply the odd numbers so
7!! = 7x5x3x1 =105.

!!! = triple factorial
Take your number and subtract 3, then subtract 3 again and keep subtracting 3 until you get to 0 or less. Then multiply all the answers together to get the triple factorial. Therefore:
8!!! = 8 x 5 x 2 = 80
10!!! = 10 x 7 x 4 x 1 = 280.

INT = the INTEGER function
If you get a number with a decimal after it, just ignore the decimal bit. Therefore:
INT(3.741) = 3
INT(19.26) = 19

We should like to apologise to any four wheel drive vehicle enthusiasts who have found this page through a search engine and are just a TINY bit disappointed.
1= 44/44
2= 4/4 + 4/4
3= (4 + 4 + 4) / 4
4= 4 + (4 - 4) x 4
5= (4 x 4 + 4) / 4
6= (4 + 4) / 4 + 4
7= 4 + 4 - 4/4
8= 4 + 4 + 4 - 4
9= 4 + 4 + 4/4
10= (44 - 4) / 4

11= 44 / (SQRT4 + SQRT4)
12= 4 x 4 - SQRT4 x SQRT4
13= 44/4 +SQRT4
14= 4 x 4 - 4 + SQRT4
15= 4 x 4 - 4/4
16= 4+ 4 +4 + 4
17= 4 x 4 + 4/4
18= 4 x 4 + 4 - SQRT4
19= 4! - 4 - 4/4
20= (4 + 4) x SQRT4 + 4

21= (44 - SQRT4) / SQRT4
22= 4 x 4 + 4 + SQRT4
23= 4! + 4/4 - SQRT4
24= 4 x 4+ 4 + 4
25= (SQRT4 + SQRT4)! + 4/4
26= 4 x 4 + 4!! + SQRT4
27= 4! + SQRT4 + 4/4
28= 4! + 4 + 4 - 4
29= 4! + 4 + 4/4
30= 4! + 4 + 4 - SQRT4

31= 4! + 4!! - 4/4
32= 4! + 4!! + 4 - 4
33= 4! + 4!! + 4/4
34= 4! + 4!! + 4 - SQRT4
35= 4! + 4!! + (4!/4!!)
36= 4! + 4 + 4 + 4
37= 4! + (4! + SQRT4) / SQRT4
38= 4! + 4!! + 4 + SQRT4
39= 4! + (4 + 4/4)!!
40= 44 - SQRT4 - SQRT4

 41= 44 - (4!/4!!)
42= 44 - 4 + SQRT4
43= 44 - 4/4
44= 44 + 4 - 4
45= 44 + 4/4
46= 44 + 4 - SQRT4
47= 44 + (4!/4!!)
48= 44 + SQRT4 + SQRT4
49= (4! x SQRT4) + 4/4
50= 44 + 4 + SQRT4

51= 4! x SQRT4 + (4!/4!!)
52= 44 + 4 + 4
53= ((4!!)!! + 4!)/ 4!! + SQRT4
54= 4! x SQRT4 + SQRT4 + 4
55= ((4!!)!! + 4!)/ 4!! + 4
56= 4! x SQRT4 + 4 + 4
57= (4!/4!!)^4 - 4!
58= 4!! x 4!! - 4 - SQRT4
59= ((4!!)!! + 4!)/ 4!! + 4!!
60= 4!! x 4!! - SQRT4 - SQRT4

61= 4!! x 4!! - (4!/4!!)
62= 4!! x 4!! - 4 + SQRT4
63= 4!! x 4!! - 4/4
64= 4!! x 4!! + 4 - 4
65= 4!! x 4!! + 4/4
66= 4!! x 4!! + 4 - SQRT4
67= 4!! x 4!! + (4!/4!!)
68= 4!! x 4!! + SQRT4 + SQRT4
69= ((4!)^SQRT4 - 4!)/ 4!!
70= 4!! x 4!! + 4 + SQRT4

 71= ((4!)^SQRT4 - 4!!)/ 4!!
72= 4!! x 4!! + 4 + 4
73= ((4!/4!!)^4 - 4!!
74= 4!! x 4!! + 4!! + SQRT4
75= ((4!)^SQRT4 + 4!)/ 4!!
76= 4! x (4!/4!!) + 4
77= (4!/4!!)^4 - 4
78= 4!! x (4!! + SQRT4) - SQRT4
79= (4!/4!!)^4 - SQRT4
80= 4!! x (4 + 4 + SQRT4)

81= (4 - 4/4)^4
82= 4!! x (4!! + SQRT4) + SQRT4
83= (4!/4!!)^4 + SQRT4
84= 4!! x (4!! + SQRT4) + 4
85= (4!/4!!)^4 + 4
86= (4 + SQRT4)! / 4!! - 4
87= ((4 + SQRT4)! - 4!) / 4!!
88= (4 + SQRT4)! / 4!! - SQRT4
89= (4!/4!!)^4 + 4!!
90= (SQRT4 + SQRT4 + SQRT4)! / 4!!

91= ((4 + SQRT4)! + 4!!) / 4!!
92= 4! x 4 - SQRT4 - SQRT4
93= 4! x 4 - (4!/4!!)
94= 4! x 4 - 4 + SQRT4
95= 4! x 4 - 4/4
96= 4! x 4 + 4 - 4
97= 4! x 4 + 4/4
98= 4! x 4 + 4 - SQRT4
99= 4! x 4 + (4!/4!!)
100= (4 + 4 + SQRT4)^SQRT4
  or 4! x 4 + SQRT4 + SQRT4

© Murderous Maths 2004

And here are all the solutions for numbers 101-200 and beyond!
101 = (4 + (4!/4!!))!! - 4
102 = ((4!!)!! + 4!)/ (SQRT4 + SQRT4)
103 = (4 + (4!/4!!))!! - SQRT4
104 = ((4!!)!! + 4!)/ 4 + SQRT4
105 = (4 + 4 - 4/4)!!
106 = ((4!!)!! + 4!)/ 4 + 4
107 = (4 + (4!/4!!))!! + SQRT4
108 = (4!! + SQRT4)^SQRT4 + 4!!
109 = (4 + (4!/4!!))!! + 4
110 = ((4!!)!! + 4!)/ 4 + 4!!

111 = 444/4
112 = (4 + 4/4)! - 4!!
113 = (4 + (4!/4!!))!! + 4!!
114 = (4 + SQRT4)! / 4!! + 4!
115 = ((4!!)!! + (4!!)!!! - 4)/4
116 = (4 + 4/4)! - 4
117 = ((4!!)!! + (4!!)!!! + 4)/4
118 = (4 + 4/4)! - SQRT4
119 = 4 x 4! + INT (SQRT(4!!)!!) + 4
120 = ((4 x 4 + 4)/ 4)!

121 = (44/4)^SQRT4
122 = (4 + 4/4)! + SQRT4
123 = 4 x 4! + INT (SQRT(4!!)!!) + 4!!
124 = 4x4! + 4! +4
125 = (((4!!)!! - 4!)/4!!) + (4!!)!!!
126 = (4^4/SQRT4) -SQRT4
127 = (((4!!)!! x 4!!) - 4!)/4!
128 = 4x4x4xSQRT4
129 = (((4!!)!! x 4!!) + 4!)/4!
130 = (4^4/SQRT4) + SQRT4

131 = (((4!!)!! + 4!)/4!!) + (4!!)!!!
132 = (4^4/SQRT4) + 4
133 = (4!! - 4/4) x INT(SQRT (4!!)!!)
134 = ((4!!)!!! x SQRT4) - 4! - SQRT4
135 = (4!! x INT(SQRT (4!!)!!)) -INT(SQRT (4!!)!!) + SQRT4
136 = (4^4/SQRT4) + 4!!
137 = (4!! x INT(SQRT (4!!)!!)) -INT(SQRT (4!!)!!) + 4
138 = (((4!)^SQRT4) - 4!)/4
139 = ((4!! + SQRT4)!!! - SQRT4)/SQRT4
140 = ((4!)^SQRT4)/4 - 4
141 = ((4!! + SQRT4)!!! + SQRT4)/SQRT4
142 = ((4!)^SQRT4)/4 - SQRT4
143 = (((4!)^SQRT4) - 4)/4
144 = (SQRT4 + SQRT4 + SQRT4) x 4!
145 = (((4!)^SQRT4) + 4)/4
146 = ((4!)^SQRT4)/4 + SQRT4
147 = (4!! x INT(SQRT(4!!)!!)) - 4 - INT(SQRT(SQRT4))
148 = ((4!)^SQRT4)/4 + 4
149 = (4!! x INT(SQRT(4!!)!!)) - (4!/4!!)
150 = (((4!)^SQRT4) + 4!)/4

151 = ((4!!)!! - (4!!)!!! - SQRT4)/SQRT4
152 = ((4!)^SQRT4)/4 + 4!!
153 = ((4!!)!! - (4!!)!!! + SQRT4)/SQRT4
154 = ((4!!)!!! x SQRT4) - 4 - SQRT4
155 = INT(SQRT((4!!)!)) - INT(SQRT((4!!)!!)) -4! -SQRT4
156 = (4! + SQRT4) x (4!/4)
157 = ((4!!)!!! x SQRT4) - (4!/4!!)
158 = ((4! - 4) x 4!!) - SQRT4
159 = ((4!!)!!! x SQRT4) - 4/4
160 = (44-4) x 4

161 = ((4!!)!!! x SQRT4) + 4/4
162 = ((4! - 4) x 4!!) + SQRT4
163 = ((4!!)!!! x SQRT4) + (4!/4!!)
164 = (4! x 4!!) - 4! - 4
165 = INT(SQRT((4!!)!)) - INT(SQRT((4!!)!!)) -4! + 4!!
166 = (4! x 4!!) - 4! - SQRT4
167 = (4!!)!! - INT(SQRT((4!!)!)) - INT(SQRT((4!!)!!)) + SQRT4
168 = (4 + 4!/4!!) x 4!
169 = ((4! + SQRT4)/SQRT4)^SQRT4
170 = (4! x 4!!) - 4! + SQRT4

171 = INT(SQRT((4!!)!)) - INT(SQRT((4!!)!!)) -4!! - SQRT4
172 = (44 x 4) - 4
173 = INT(SQRT((4!!)!)) - 4! -(4!/4!!)
174 = (44 x 4) - SQRT4
175 = INT(SQRT((4!!)!)) - 4! -4/4
176 = 44 x SQRT4 x SQRT4
177 = INT(SQRT((4!!)!)) - 4! +4/4
178 = (44 x 4) + SQRT4
179 = ((4!!)!! - 4! - SQRT4)/SQRT4
180 = (4! x 4!!) - 4!! - 4
 181 = ((4!!)!! - 4! + SQRT4)/SQRT4
182 = (4! x 4!!) - 4!! - SQRT4
183 = INT(SQRT((4!!)!)) - INT(SQRT((4!!)!!)) + SQRT4
184 = (4! x 4!!) - 4 - 4
185 = (4 + (4!/4!!))!! + (4!!)!!!
186 = (4! x 4!!) - 4 - SQRT4
187 = ((4!!)!! - 4!! - SQRT4)/SQRT4
188 = (4! x 4!!) - (SQRT4 x SQRT4)
189 = (4! x 4!!) - (4!/4!!)
190 = (4! x 4!!) - (4/SQRT4)

191 = (4! x 4!!) - (4/4)
192 = (4! x 4!!) x 4/4
193 = (4! x 4!!) + (4/4)
194 = (4! x 4!!) + (4/SQRT4)
195 = (4! x 4!!) + (4!/4!!)
196 = (4!! + 4 + SQRT4)^SQRT4
197 = ((4!!)!! +4!! +SQRT4)/SQRT4
198 = (4! x 4!!) + 4 + SQRT4
199 = INT(SQRT((4!!)!)) - (SQRT4 x SQRT4)/4
200 = (4! x 4!!) + 4 + 4

And here are just a few more...

201 = INT(SQRT((4!!)!)) + (SQRT4 x SQRT4)/4
202 = ((4!!)!! + 4! - 4)/SQRT4
203 = ((4!!)!! + 4! - SQRT4)/SQRT4
204 = ((4!!)!! + (SQRT4 x SQRT4)!)/SQRT4
205 = ((4!!)!! + 4! + SQRT4)/SQRT4
206 = ((4!!)!! + 4! + 4)/SQRT4
207 = INT(SQRT((4!!)!)) + 4 + 4!/4!!
208 = (4! x 4!!) + (4 x 4)
209 = INT(SQRT((4!!)!)) + 4!! +4/4
210 = (4 + 4!/4!!)!! x SQRT4)
211 = INT(SQRT((4!!)!)) + 4!! + 4!/4!!
212 = INT(SQRT((4!!)!)) + 4+ 4 +4

© Murderous Maths 2004

Many thanks to Sunny (Ana Marin) and Michael Jones who first
supplied these answers to us way back in 2004.

There is also an answer using the LOG function to create ANY number!

All you have to do is increase the number of square root signs in the bracket.

Pray tell, what is this sorcery?

All is explained here by the brilliant Alex Bellos...

These equations can seem quite complicated to people who are not well versed in maths. Even a complicated R&D tax credit calculation can be too confusing for some people without the assistance of a R&D tax credit calculator online.

To the Puzzles Page

Murderous Maths Home Page