Take the digits 2, 0, 0 and 3. Make equations equating to all the integers from 1 to 150 using these digits according to the following rules:-

a) The above digits are the only digits to be used and no other digits should appear anywhere in the equation (except on the side where the answer will be).

b) Use of any mathematical symbols are allowed.

c) The digits 2, 0, 0 and 3 should appear in the given order in the equation. e.g - 0 + 2 + 3 + 0 = 5 is not acceptable.

d) When using the mathematical symbols try using the most simplest forms as much as possible.

I managed to generate all values 0 to 150 using only the following:
+ - * / ! ^ ( ) sqrt sin cos tan floor ceil

0= 2*0*0*3
1= (2+0)^(0*3)
2= 2+0*0*3
3= 2*0*0+3
4= 20^0+3
5= 2+0+0+3
6= (2+0+0)*3
7= 20^0+3!
8= 2+0+0+3!
9= (2+0+0!)*3

10= 20/(-(0!)+3)
11= (2+0!)!-0!+3!
12= (2+0!+0!)*3
13= (2+0!)!+0!+3!
14= 2*(0+0!+3!)
15= ((2+0!)!-0!)*3
16= 2^(0+0!+3)
17= 20+0-3
18= 20+0!-3
19= 20-(0*3)!

20= 20+0*3
21= 20+(0*3)!
22= 20-0!+3
23= 20+0+3
24= 20+0!+3
25= 20-0!+3!
26= 20+0+3!
27= 20+0!+3!
28= (floor sqrt 20)+(0!+3)!
29= (ceil sqrt 20)+(0!+3)!

30= (2+0!)!+(0!+3)!
31= ceil [-2*(tan (0!+0!))/sin 3]
32= 2^(0!+0!+3)
33= (2+0!)*floor [(tan (0!))/(sin 3)]
34= 2+0!+ceil [(tan tan (0!))/(sqrt 3)]
35= -2+floor [(tan tan (0!))/(-(0!)+3)]
36= (2+0!)!*(0+3)!
37= ceil [cos 2+(tan tan (0!))/(-(0!)+3)]
38= floor [sqrt 2+(tan tan (0!))/(-(0!)+3)]
39= 2+floor [(tan tan (0!))/(-(0!)+3)]

40= 20*(-(0!)+3)
41= -2+0+floor [(tan tan (0!))/(sqrt 3)]
42= ((2+0!)!+0!)*3!
43= 2*0+floor [(tan tan (0!))/(sqrt 3)]
44= 20+(0!+3)!
45= 2+0+floor [(tan tan (0!))/(sqrt 3)]
46= 2*(-(0!)+(0!+3)!)
47= 2+ceil [(tan tan (0!))/(tan (0!))]-3
48= (2+0)*(0!+3)!
49= floor [2*(tan tan (0!))/(0+3)]

50= 2*(0!+(0!+3)!)
51= -2+floor[(tan tan (0!))/(tan (0!))]+3!
52= 2+floor[(tan tan (0!))/(tan (0!))]+3
53= 2+ceil[(tan tan (0!))/(tan (0!))]+3
54= (ceil[-(tan 2)]^(0!+0!))*3!
55= -2+0+ceil[(tan tan (0!))/(sqrt sqrt 3)]
56= 2*0+floor[(tan tan (0!))/(sqrt sqrt 3)]
57= (20-0!)*3
58= 2+0+floor[(tan tan (0!))/(sqrt sqrt 3)]
59= 2+0+ceil[(tan tan (0!))/(sqrt sqrt 3)]

60= 20*(0+3)
61= floor[(sqrt 2)*(tan tan (0!))/(tan (0!))]-3!
62= -2+(0!+0!)^(3!)
63= (20+0!)*3
64= (2+0+0)^(3!)
65= -2-0!+floor[tan tan (0!)]-3!
66= 2+(0!+0!)^(3!)
67= -2+0+ceil[tan tan (0!)]-3!
68= 2*0+floor[tan tan (0!)]-3!
69= 2*0+ceil[tan tan (0!)]-3!

70= -2-0+ceil[tan tan (0!)]-3
71= 2*0+floor[tan tan (0!)]-3
72= (2+0!+0!)!*3
73= 2+floor[tan tan (0!)]+0-3
74= 2+ceil[tan tan (0!)]+0-3
75= -2+floor[tan tan (0!)]+0+3
76= 2+floor[tan tan (0!)]+0*3
77= 2*0+floor[tan tan (0!)]+3
78= 2*0+ceil[tan tan (0!)]+3
79= 2+floor[tan tan (0!)]+0+3

80= 2+ceil[tan tan (0!)]+0+3
81= (2+0!)^(0!+3)
82= 2+floor[tan tan (0!)]+0+3!
83= 2+ceil[tan tan (0!)]+0+3!
84= 2+ceil[tan tan (0!)]+0!+3!
85= floor[(sqrt sqrt 2)*(tan tan (0!))]+0-3
86= ceil[(sqrt sqrt 2)*(tan tan (0!))]+0-3
87= ceil[(sqrt sqrt 2)*(tan tan (0!))]+0!-3
88= floor[(sqrt sqrt 2)*(tan tan (0!))]+0*3
89= ceil[(sqrt sqrt 2)*(tan tan (0!))]+0*3

90= floor[(sqrt sqrt 2)*(tan tan (0!))]-0!+3
91= 20+floor[tan tan (0!)]-3
92= 20+ceil[tan tan (0!)]-3
93= floor[20*tan (0!)]*3
94= ceil[20*(tan (0!))*3]
95= 20-floor[(tan tan (0!))/(cos 3)]
96= ceil[20*tan (0!)]*3
97= 20+floor[tan tan (0!)]+3
98= 20+ceil[tan tan (0!)]+3
99= ceil[-(cos 2)*(tan tan (0!))+0!]*3

100= 20*(-(0!)+3!)
101= 2+0+ceil[(tan tan (0!))*(sqrt sqrt 3)]
102= floor[(sqrt 2)*(tan tan (0!))]+0-3
103= ceil[(sqrt 2)*(tan tan (0!))]+0-3
104= ceil[(sqrt 2)*(tan tan (0!))]+0!-3
105= floor[(sqrt 2)*(tan tan (0!))]+0*3
106= ceil[(sqrt 2)*(tan tan (0!))]+0*3
107= ceil[(sqrt 2)*(tan tan (0!))]+(0*3)!
108= floor[(sqrt 2)*(tan tan (0!))]+0+3
109= ceil[(sqrt 2)*(tan tan (0!))]+0+3

110= ceil[(sqrt 2)*(tan tan (0!))]+0!+3
111= floor[(sqrt 2)*(tan tan (0!))]+0+3!
112= ceil[(sqrt 2)*(tan tan (0!))]+0+3!
113= ceil[(sqrt 2)*(tan tan (0!))]+0!+3!
114= (20+0!)*3!
115= -2+0+ceil[(tan tan (0!))*(sqrt sqrt (3!))]
116= 2*0+floor[(tan tan (0!))*(sqrt sqrt (3!))]
117= ((2+0!)!-0!)!-3
118= -2+(0!+0!+3)!
119= -2+0!+(-(0!)+3!)!

120= 20*(0+3!)
121= 2-0!+(-(0!)+3!)!
122= 2+(0!+0!+3)!
123= ((2+0!)!-0!)!+3
124= -(2+0!)!+ceil[(tan tan (0!))*(sqrt 3)]
125= ((2+0!)!-0!)^3
126= (20+0!)*3!
127= -2-0+floor[(tan tan (0!))*(sqrt 3)]
128= 2^(0+0!+3!)
129= 2*0+floor[(tan tan (0!))*(sqrt 3)]

130= 2*0+ceil[(tan tan (0!))*(sqrt 3)]
131= 2+0+floor[(tan tan (0!))*(sqrt 3)]
132= 2+0+ceil[(tan tan (0!))*(sqrt 3)]
133= 2+0!+ceil[(tan tan (0!))*(sqrt 3)]
134= -2+ceil[(tan tan (0!))/(cos (0!))]-3
135= -2+ceil[(tan tan (0!))/(cos (0!))-(sqrt 3)]
136= floor[(sqrt 2)+(tan tan (0!))/(cos (0!))]-3
137= 2+floor[(tan tan (0!))/(cos (0!))]-3
138= 2+ceil[(tan tan (0!))/(cos (0!))]-3
139= -2+floor[(tan tan (0!))/(cos (0!))]+3

140= 20*(0!+3!)
141= 2*floor[tan tan (0!)]-0!-3!
142= 2*floor[tan tan (0!)]+0-3!
143= floor[2*(tan tan (0!))]-0-3!
144= (2+0!+0!)!*3!
145= 2*floor[tan tan (0!)]+0-3
146= floor[2*(tan tan (0!))]+0-3
147= 2*ceil[tan tan (0!)]+0-3
148= 2*floor[tan tan (0!)]+0*3
149= floor[2*(tan tan (0!))]+0*3
150= 2*ceil[tan tan (0!)]+0*3
Edited on December 2, 2003, 11:40 am

Posted by Brian Smith on 2003-04-24 06:15:39