mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2019-01-06, 17:14   #1
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT)

26·89 Posts
Default M51 arithmetic

Most of us will have heard of the 4 4s puzzle where you try to create numbers using only the number 4 and various operators. Mersenneforum has multiple threads where variants have been explored.
Having discovered it again so soon after a new Mersenne prime has been found I thought it would be a fun challenge to use the numbers from the new exponent 82,589,933.

Initially it would be nice to keep it simple just using the operators +, -, * and / along with brackets to see how far we can get. Other operators will be added later once they are needed(maybe a scoring system could be worked out).
All digits must be used. Bonus points(I suspect it will be too hard very quickly) for using the digits in the correct order.

I will start us off with a few examples:

Code:
0 = (8+2+5+8+9+9)*(3-3)
1 = 8-2+5+8-9-9+3-3
2 = 8-2+5+8-9-9+(3/3)
3 = 8-2+5-8-9+9+3-3
edit:
Solutions so far:
Code:
0 = (8+2+5+8+9+9)*(3-3)
1 = 8-2+5+8-9-9+3-3
2 = 8-2+5+8-9-9+(3/3)
3 = 8-2+5-8-9+9+3-3
4 = 8/2+5*8*9*9*(3-3)
5 = 8+2-5+8*9*9*(3-3)
6 = 8+2-5-8+9+9*(3-3)
7 = 8+2+5-8-9+9-3+3
8 = 8+2*5*8*9*9*(3-3)
9 = (8-2-5+8)*(9/9)*(3/3)
10 = (8-2)+(5+8-9*(9/(3*3))
11 = (8+2)/5 + 8+(9/9)*(3/3)
12 = (8+2-5)+8*(9/9)-(3/3)
13 = (8+2-5)+8*(9/9)*(3/3)
14 = (8+2-5)+8*(9/9)+(3/3)
15 = (8+2-5)+8+9/9+3/3
16 = (8+2+5-8+9)*(9/(3*3))
17 = (8+2+5-8+9+(9/(3*3))
18 = (8-2-5)*(8+9)+(9/(3*3))
19 = (8-2-5)+(8+9)+(9/(3*3))
20 = 8+2+5+(8-9)+(9/3)+3
21 = (8+2+5-8)*(9/(9-3-3))
22 = (8+2+5+8)-(9/9)*(3/3)
23 = (8+2+5+8)*(9/9)*(3/3)
24 = (8+2+5+8)+(9/9)*(3/3)
25 = ((8+2)*5)-8-9-9+(3/3)
26 = (8*2+5+8)-(9/(9-3-3))
27 = (8*2+5+8)-(9/9)-(3/3)
28 = (8*2+5+8)-((9/9)*(3/3))
29 = (8*2+5+8)*(9/9)*(3/3)
30 = (8*2+5+8)+((9/9)*(3/3))
31 = (8*2+5+8)+(9/9)+(3/3)
32 = (8+2+5+8+9)*(9/(3*3))
33 = (8+2+5+8+9)+(9/(3*3))
34 = 8-2+5+8+9+9/3+3
35 = 8+2+5+8+9+9-3-3
36 = 8-2+5+8+9+9-3/3
37 = 8-2+5*8+9-9-3*3
38 = 8+2+5+8+9+9/3+3
39 = (8+2)*5-8-9+(9/3)+3
40 = (8+2)*5-8-(9/9)-(3/3)
41 = (8+2)*5-8-((9/9)*(3/3))
42 = (8+2)*5-8+(9/9)-(3/3)
43 = (8+2)*5-8+((9/9)*(3/3))
44 = (8+2)*5-8+(9/9)+(3/3)
45 = (8+2)*5-8+(9/(9-3-3))
46 = (8+2+5+8)*((9/9)+(3/3))
47 = 8+2+5+8+9+9+3+3
48 = 8*(2+5+8-9)*(9/(3*3))
49 = (8+2+5-8)*((9/9)+3+3)
50 = (8+2)*5+8-9+9/3/3
51 = (8+2)*5-8+9*9/3/3
52 = (8+2)*5-8+9+9/3/3
53 = 8 * 2 * 5 - 8 - 9 - 9 - 3/3
54 = 8 * 2 * 5 - 8 - 9 - 9 - (3 - 3)
55 = 8 * 2 * 5 - 8 - 9 - 9 + 3/3
56 = 8 * 2 + 5 * 8 - 9/9 + 3/3
57 = (8+2)*5+8-(9/9*3/3)
58 = (8+2)*5+8+(9-9+3-3)
59 = (8+2)*5+8 + (9/9*3/3)
60 = (8+2)*5+8 + (9/9+3/3)
61 = (8+2)*5+8 + (9-9/3-3)
62 = (8+2)*5+8 + ((9+9/3)/3)
63 = (8+2)*5+8 - (9/9-3-3)
64 = (8+2)*5+8 + (9-9+3+3)
65 = (8+2)*5+8 + (9/9+3+3)
66 = (8+2)*5+8 + (9-9/3/3)
67 = (8+2)*5+8 + (9*9/3/3)
68 = (8+2)*5+8 + (9+9/3/3)
69 = ((8 - 2 + 5 + 8 + (9/9) + 3)) * 3
70 = (8-2)*(5+8)-(9-9/3/3)
71 = (8-2)*(5+8)-(9/9+3+3)
72 = (8-2)*(5+8)-(9-9+3+3)
73 = (8-2)*(5+8)+(9/9-3-3)
74 = (8-2)*(5+8)-((9+9/3)/3)
75 = (8-2)*(5+8)-(9-9/3-3)
76 = (8-2)*(5+8)-(9/9+3/3)
77 = (8-2)*(5+8)-(9/9*3/3)
78 = (8-2)*(5+8)-(9-9+3-3)
79 = (8-2)*(5+8)+(9/9*3/3)
80 = (8-2)*(5+8)+(9/9+3/3)
81 = (8-2)*(5+8)+(9-9/3-3)
82 = (8-2)*(5+8)+((9+9/3)/3)
83 = (8-2)*(5+8)-(9/9-3-3)
84 = (8-2)*(5+8)+(9-9+3+3)
85 = (8-2)*(5+8)+(9/9+3+3)
86 = (8-2)*(5+8)+(9-9/3/3)
87 = (8-2)*(5+8)+(9*9/3/3)
88 = (8-2)*(5+8)+(9+9/3/3)
89 = (8-2-5)*8+(9*9)*(3/3)
90 = 8*2*5 + 8 + 9/9 + 3/3
91 = (8*2*5/8)*9 +9/3/3
92 = 8*2*5+8+((9+9/3)/3)
93 = 8*2*5+8-(9/9-3-3)
94 = 8*2*5+8-9+9+3+3
95 = 8*2*5+8+9/9+3+3
96 = 8*2*5-8+9+9+3+3
97 = (8+2)*(5+8+9-9-3)-3
98 = -8-2+(5+8)*9-9+3-3
99 = 8/2+5+8+9*9+3/3
100 = 8+2-5+8+9*9+3+3
101 = 8*2+5+8+9*9-3*3
102 = 8*(2+5+8)-9-9+3-3
103 = (8+2)*(5+8+9-9-3)+3
104 = -8+(2*5)+(8*9)+(9*3)+3
105 = 8+2+5*(8+9+(9-3)/3)
106 = 8-2+5+8+9*9+3+3
107 = 8+(2×5−8+9)×9−3+3
108 = 8+2*5+8+9*9+3/3
109 = 8*2-5+8+9*9+3*3
110 = 8*2+5+8+9*9+3-3
111 = 8-2+5*(8+9+(9+3)/3)
112 = -8+2+5*(8+9+9-3)+3
113 = 8+2+5*(8+9+9/3)+3
114 = -8/2+5*(8+9+9-3)+3
115 = 8+2+5*(8+9+(9+3)/3)
116 = 8*2+5*(8+9+9-3-3)
117 to 133 = 8*(2+5+8) + L4D[-3 to 13]
134 to 143 = (8+2)*(5+8) + L4D[4 to 13]
144 to 157 = 8*(2*5+8) + L4D[0 to 13]
158 to 173 = 8/(2/(5*8)) + L4D[-2 to 13]
174 to 181 = (8*2+5)*8 + L4D[6 to 13]
182 to 205 = 8*(2-5)*8 + L4D[-10 to 13]
206 to 221 = 8*2*(5+8) + L4D[-2 to 13]
222 = 8*2*(5/(8/(9*9/3))-3)
223 = 8+2*5*(8+9*9/(3+3))
224 = 8*2*(5+8+9-(9-3/3))
225 = 8/(2/(5/(8/(9+9*3*3))))
226 = 8*2*(5+8+9/(9-3/3))
227 to 253 = (8-2)*5*8 + L4D[-13 to 13]
254 to 259 = (8+2+5)*(8+9) + L3D[-1 to 4]
260 to 265 = (8+2+5)*(8+9) + L3D[-1 to 4]
266 to 268 = (8+2+5)*(8+9) + L3D[2 to 4]
269 to 273 = (8+2+5)*(8+9) + L3D[1 to 4]
274 = (8+2+5)*(8+9) + L3D[4]
275 = 8*2+5+8+9*9*3+3
276 = (8-2)*5*8+9*(9+3)/3
277 = 8*(2*(5+8)+9) + L3D[-3]
278 = (8-2)*5+8+9*9*3-3
279 = -(8+2-5*8)*9 + L3D[9]
280 = 8+2*(5+8)+9*9*3+3
281 = 8*(2*(5+8)+9) + L3D[1]
282 = (8+2)*5-8+9*9*3-3
283 = (8*2)*(5+8)+9*9-3-3
284 = 8*(2*(5+8)+9) + L3D[4]
285 to 292 = (8-(2-5)*8)*9 + L3D[-3 to 4]
293 to 298 = (8-2)*(5*8+9) + L3D[-1 to 4]
299 to 317 = 8*(-2+5*8) + L4D[-13 to 13]
318 to 319 = 8*(2+5*8) + L4D[-18 to -17]
320 = 8*2*5*(8-L4D[4])
321 = 8*(2+5*8) + L4D[-15]
322 = 8*(-2+5*8) + L4D[18]
323 to 349 = 8*(2+5*8) + L4D[-13 to 13]
350 to 356 = 8*2*(5+8+9) + L3D[-3 to 4]
357 = 8-2+5*8*9 + L3D[-9]
358 = -8+2+5*8+9*(9+3)*3
359 = -8/2+5*8*9 + L3D[3]
360 = 8-2+5*8*9+L3D[-6]
361 = 8+2+5*8*9+L3D[-9]
362 to 370 = 8-2+5*8*9 + L3D[-4 to 4]
371 to 374 = 8+2+5*8*9 + L3D[1 to 4]
375 to 380 = 8*2+5*8*9 + L3D[-1 to 4]
381 = (8+2)*5*8 + L4D[-19]
382 to 390 = 8+(2+5*8)*9 + L3D[-4 to 4]
391 to 413 = (8+2)*5*8 + L4D[-9 to 13]
414 to 418 = (8-2+5*8)*9 + L3D[0 to 4]
419 = (8+2)*5*8 + L4D[19]
420 = (8-2+5*8)*9 + L3D[6]
421 = (8+2)*5*8 + L4D[21]
422 to 424 = (8-2+5*8)*9 + L3D[8 to 10]
425 = 8+2+5*(8+9*9-3-3)
426 = ((8+2)+5*8)*9 - 9*3+3
427 = 8*(2+5)*8 + L4D[-21]
428 = (-8+(2+5)*8)*9 +L3D[-4]
429 to 431 = 8*(2+5)*8 + L4D[-19 to -17]
432 = 8/2*(5+8)*9 - (9+3)*3
433 = 8*(2+5)*8 + L4D[-15]
434 to 461 = 8*(2+5)*8 + L4D[-13 to 13]
462 = 8/2*(5+8)*9 + L3D[-6]
463 = (8+2)*(5*8+(9+9)/3)+3
464 to 472 = 8/2*(5+8)*9 + L3D[-4 to 4]
473 = 8+2+5*(8+9*9+3)+3
474 = (8*2+5*8)*9+L3D[-30]
475 = (8+2)*(5*8+9) + L3D[-15]
476 = 8+(2+5)*8*9 + L3D[-36]
477 = 8/(2/(5+8)/9)+9-3+3
478 = 8*2*(5*8-9) + L3D[-18]
479 = (8+2)*5+8*9*(9-3)-3
480 to 482 = (8+2)*(5*8+9) + L3D[-10 to -8]
483 = 8/(2/(5+8)/9) + L3D[15]
484 = (8+2)*(5*8+9) + L3D[-6]
485 = (8+2)*5+8*9*(9-3)+3
486 to 494 = (8+2)*(5*8+9) + L3D[-4 to 4]
495 = (8*2+5*8)*9 + L3D[-9]
496 = (8+2)*(5*8+9) + L3D[6]
497 = 8*2*(5*8-9) + L3D[1]
498 to 500 = (8+2)*(5*8+9) + L3D[8 to 10]
501 to 504 = (8*2+5*8)*9 + L3D[-3 to 0]
505 = (8+2)*(5*8+9) + L3D[15]
506 to 507 = (8*2+5*8)*9 + L3D[2 to 3]
508 = (8+2)*(5*8+9) + L3D[18]
509 = (8-2)*5*(8+9) + L3D[-1]
510 = (8*2+5*8)*9 + L3D[6]
511 = 8*2*(5*8-9) + L3D[15]
512 to 513 = (8*2+5*8)*9 + L3D[8 to 9]
514 = (8+2)*(5*8+9) + L3D[24]
515 = 8+(2+5)*8*9 + L3D[3]
516 = (8-2)*5*(8+9) + L3D[6]
517 = (8+2)*(5+8)*(9/9+3)-3
518 = (8-2)*5*(8+9) + L3D[8]
519 = (8*2+5*8)*9 + L3D[15]
520 = (8+2)*(5*8+9) + L3D[30]
521 = 8+(2+5)*8*9 + L3D[9]
522 = (8*2+5*8)*9 + L3D[18]
523 = (8+2)*(5+8)*(9/9+3)+3

525 = (8-2)*5*(8+9) + L3D[15]
526 = (8+2)*(5*8+9) + L3D[36]
527 = 8+(2+5)*8*9 + L3D[15]
528 = (8*2+5*8)*9 + L3D[24]

532 = 8*2*(5*8-9) + L3D[36]

534 = (8*2+5*8)*9 + L3D[30]

536 = 8+(2+5)*8*9 + L3D[24]

540 = (8*2+5*8)*9 + L3D[36]

542 = 8+(2+5)*8*9 + L3D[30]

546 = (8-2)*5*(8+9) + L3D[36]

548 = 8+(2+5)*8*9 + L3D[36]

666 = (8*2*5-8)*9+9+3*3
Last 4 digits:
Code:
0 = (9-9+3-3)
1 = (9/9*3/3)
2 = (9/9+3/3)
3 = (9-9/3-3)
4 = ((9+9/3)/3)
5 = -(9/9-3-3)
6 = (9-9+3+3)
7 = (9/9+3+3)
8 = (9-9/3/3)
9 = (9*9/3/3)
10 = (9+9/3/3)
11 = 9+(9-3)/3
12 = 9+9-3-3
13 = 9+(9+3)/3

15 = -9+9*3-3

17 = 9+9-3/3
18 = 9+9+3-3
19 = 9+9+3/3

21 = -9+9*3+3

24 = 9*9/3-3

30 = 9*9/3+3

33 = 9+9*3-3

36 = 9*(9+3)/3

39 = 9+9*3+3
Last 3 digits:
Code:
0 = 9-3*3
1 = 9/3/3
2 = (9-3)/3
3 = 9-3-3
4 = (9+3)/3

6 = 9/3+3

8 = 9-3/3
9 = 9+3-3
10 = 9+3/3

15 = 9+3+3

18 = 9+3*3

24 = 9*3-3

30 = 9*3+3

36 = (9+3)*3

Last fiddled with by henryzz on 2019-02-17 at 16:59
henryzz is offline   Reply With Quote
Old 2019-01-06, 17:37   #2
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

22×17×127 Posts
Default

4 = 8/2+5*8*9*9*(3-3)
5 = 8+2-5+8*9*9*(3-3)
6 = 8+2-5-8+9+9*(3-3)


(hehe, just ugly hack popped to my head in half second, looking at how you made zero)

Last fiddled with by LaurV on 2019-01-06 at 17:41
LaurV is offline   Reply With Quote
Old 2019-01-06, 17:38   #3
Brownfox
 
Brownfox's Avatar
 
Dec 2017

2·29 Posts
Default

4 = 8+2+5+8-9-9-(3/3)
Brownfox is offline   Reply With Quote
Old 2019-01-06, 17:55   #4
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts
Default

Quote:
Originally Posted by LaurV View Post
4 = 8/2+5*8*9*9*(3-3)
5 = 8+2-5+8*9*9*(3-3)
6 = 8+2-5-8+9+9*(3-3)
7=8+2+5-8-9+9-3+3
8=8+2*5*8*9*9*(3-3)
9=(8-2-5+8)*(9/9)*(3/3)
10=(8-2)+(5+8-9*(9/(3*3))
11=(8+2)/5 + 8+(9/9)*(3/3)
12=8+2-5-8+9+9+3+3
13=(8+2-5)+8*(9/9)*(3/3)
14=(8+2-5)+8*(9/9)+(3/3)
15=(8+2-5)+8+9/9+3/3
16=(8+2+5-8+9)*(9/(3*3))
17=(8+2+5-8+9+(9/(3*3))
18=(8-2-5)*(8+9)+(9/(3*3))
19=(8-2-5)+(8+9)+(9/(3*3))
20=8+2+5+(8-9)+(9/3)+3
21= (8+2+5-8)*(9/(9-3-3))
22=(8+2+5+8)-(9/9)*(3/3)
23=(8+2+5+8)*(9/9)*(3/3)
24=(8+2+5+8)+(9/9)*(3/3)
25=((8+2)*5)-8-9-9+(3/3)
26=(8*2+5+8)-(9/(9-3-3))
27=(8*2+5+8)-(9/9)-(3/3)
28=(8*2+5+8)-((9/9)*(3/3))
29=(8*2+5+8)*(9/9)*(3/3)
30=(8*2+5+8)+((9/9)*(3/3))
31=(8*2+5+8)+(9/9)+(3/3)
32=(8+2+5+8+9)*(9/(3*3))
33=(8+2+5+8+9)+(9/(3*3))
34=(8-2+5+8+9)+(9-3-3)
35=(8-2+5-8+9)+(9+3-3)
36=(8-2+5-8+9)+9+3+3

Last fiddled with by science_man_88 on 2019-01-06 at 18:37 Reason: adding a few more each edit. doh errors.
science_man_88 is offline   Reply With Quote
Old 2019-01-06, 18:27   #5
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT)

26×89 Posts
Default

22 = 8+2*(5+8)-9-9+3+3
henryzz is offline   Reply With Quote
Old 2019-01-06, 18:34   #6
Brownfox
 
Brownfox's Avatar
 
Dec 2017

2×29 Posts
Default

26 = 8+(2*5)+8+9-9+3-3
27 = 8+(2*5)+8-9+9+(3/3)
Brownfox is offline   Reply With Quote
Old 2019-01-07, 06:13   #7
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

863610 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
34=(8-2+5+8+9)+(9-3-3) huh?
35=(8-2+5-8+9)+(9+3-3) huh?
36=(8-2+5-8+9)+9+3+3 huh?
I took it from the end, but stopped after 3 wrong out of 3... 100% failure rate...
LaurV is offline   Reply With Quote
Old 2019-01-07, 09:45   #8
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT)

164016 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
7=8+2+5-8-9+9-3+3
8=8+2*5*8*9*9*(3-3)
9=(8-2-5+8)*(9/9)*(3/3)
10=(8-2)+(5+8-9*(9/(3*3))
11=(8+2)/5 + 8+(9/9)*(3/3)
12=8+2-5-8+9+9+3+3
13=(8+2-5)+8*(9/9)*(3/3)
14=(8+2-5)+8*(9/9)+(3/3)
15=(8+2-5)+8+9/9+3/3
16=(8+2+5-8+9)*(9/(3*3))
17=(8+2+5-8+9+(9/(3*3))
18=(8-2-5)*(8+9)+(9/(3*3))
19=(8-2-5)+(8+9)+(9/(3*3))
20=8+2+5+(8-9)+(9/3)+3
21= (8+2+5-8)*(9/(9-3-3))
22=(8+2+5+8)-(9/9)*(3/3)
23=(8+2+5+8)*(9/9)*(3/3)
24=(8+2+5+8)+(9/9)*(3/3)
25=((8+2)*5)-8-9-9+(3/3)
26=(8*2+5+8)-(9/(9-3-3))
27=(8*2+5+8)-(9/9)-(3/3)
28=(8*2+5+8)-((9/9)*(3/3))
29=(8*2+5+8)*(9/9)*(3/3)
30=(8*2+5+8)+((9/9)*(3/3))
31=(8*2+5+8)+(9/9)+(3/3)
32=(8+2+5+8+9)*(9/(3*3))
33=(8+2+5+8+9)+(9/(3*3))
34=(8-2+5+8+9)+(9-3-3)
35=(8-2+5-8+9)+(9+3-3)
36=(8-2+5-8+9)+9+3+3
Copied all these into excel. 12 is wrong(21) as are 34, 35, 36. The rest are right apart from unbalanced brackets in 10 and 17
henryzz is offline   Reply With Quote
Old 2019-01-07, 10:47   #9
axn
 
axn's Avatar
 
Jun 2003

467210 Posts
Default

34=8-2+5+8+9+9/3+3
36=8-2+5+8+9+9-3/3
EDIT:-
35=8+2+5+8+9+9-3-3
38=8+2+5+8+9+9/3+3
37=8-2+5*8+9-9-3*3

Last fiddled with by axn on 2019-01-07 at 10:54
axn is offline   Reply With Quote
Old 2019-01-07, 11:11   #10
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

203008 Posts
Default

Quote:
Originally Posted by henryzz View Post
Copied all these into excel. 12 is wrong(21) as are 34, 35, 36. The rest are right apart from unbalanced brackets in 10 and 17
yeah I found the errors myself hence the edit reason of doh errors. 12=(8+2-5)+8*(9/9)-(3/3) though. beyond 47 addition won't work without multiplication as well.
science_man_88 is offline   Reply With Quote
Old 2019-01-07, 11:29   #11
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default

Quote:
Originally Posted by axn View Post
38=8+2+5+8+9+9/3+3
39=(8*2*5)-8-9+(9/3)+3
40=(8*2*5)-8-(9/9)-(3/3)
41=(8*2*5)-8-((9/9)*(3/3))
42=(8*2*5)-8+(9/9)-(3/3)
43=(8*2*5)-8+((9/9)*(3/3))
44=(8*2*5)-8+(9/9)+(3/3)
45=(8*2*5)-8+(9/(9-3-3))
46=(8+2+5+8)*((9/9)+(3/3))
47=8+2+5+8+9+9+3+3 // combined only from here.
science_man_88 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Antipodean arithmetic ewmayer Science & Technology 34 2015-10-03 01:31
Some arithmetic... science_man_88 science_man_88 11 2014-07-30 22:53
modular arithmetic science_man_88 Miscellaneous Math 42 2011-07-26 02:02
Simple Arithmetic! mfgoode Puzzles 82 2007-05-02 08:13
Check my arithmetic R.D. Silverman Factoring 3 2006-06-05 23:49

All times are UTC. The time now is 23:03.

Fri Aug 14 23:03:07 UTC 2020 up 1 day, 19:38, 0 users, load averages: 1.02, 1.11, 1.19

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.