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196 UND ANDERE LYCHREL ZAHLEN

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Die folgenden sind einige der "statistische" Dinge, die ich über die einzelnen Datensätze gefunden haben.

Tabelle Legend

"Iteration Count " ist die erste Iteration, dass ein bestimmter Datensatz erzeugt. Gäbe es mehr als eine Iteration, die sagen einem 6 Millionen stellige Zahl produziert, ich habe nur gerettet das erste.

Die Formel I für die "Iteration / Digit Ratio" verwendet wird: I / D.

Die Formel I für die "Digit-Pairs Verarbeitete" verwendet wird: Digits (Iterationen +7) / 2

.

Stelligen Meilenstein Iteration Graf Iteration / Stellige Verhältnis Ziffernpaare Verarbeitete
1 Million 2,415,836  2 .4158360000  1,207,921,500,000
2 Million 4,830,292 2 .4151460000 4,830,299,000,000
3 Million 7,245,928 2 .4153093333 10,868,902,500,000
4 Million 9,662,071 2 .4155177500 19,324,156,000,000
5 Million 12,078,865 2 .4157730000 30,197,180,000,000
6 Million 14,495,294 2 .4158823333 43,485,903,000,000
7 Million 16,911,863 2 .4159804286 59,191,545,000,000
8 Million 19,327,667 2 .4159583750 77,310,696,000,000
9 Million 21,744,278 2 .4160308889 97,849,282,500,000
10 Million 24,159,531 2 .4159531000 120,797,690,000,000
11 Million 26,574,642 2 .4158765455 146,160,569,500,000
12 Million 28,991,159 2 .4159299167 173,946,996,000,000
13 Million 31,408,295 2 .4160226923 204,153,963,000,000
14 Million 33,824,775 2 .4160553571 236,773,474,000,000
15 Million 36,240,602 2 .4160401333 271,804,567,500,000
16 Million 38,655,227 2 .4159516875 309,241,872,000,000
17 Million 41,070,365 2 .4159038235 349,098,162,000,000
18 Million 43,487,182 2 .4159545556 391,384,701,000,000
19 Million 45,901,512 2 .4158690526 436,064,430,500,000
20 Million 48,316,988 2 .4158494000 483,169,950,000,000
21 Million 50,732,545 2 .4158354762 532,691,796,000,000
22 Million 53,148,015 2 .4158188636 584,628,242,000,000
23 Million 55,565,809 2 .4159047391 639,006,884,000,000
24 Million 57,982,436 2 .4159348333 695,789,316,000,000
25 Million 60,398,130 2 .4159252000 754,976,712,500,000
26 Million 62,816,046 2 .4160017692 816,608,689,000,000
27 Million 65,231,462 2. 4159800741 880,624,831,500,000
28 Million 67,648,377 2. 4160134643 947,077,376,000,000
29 Million 70,067,270 2. 4161127586 1,015,975,516,500,000
30 Million 72,482,579 2. 4160859667 1,087,238,790,000,000
31 Million 74,899,358 2. 4161083226 1,160,940,157,500,000
32 Million 77,314,955 2. 4160923438 1,237,039,392,000,000
33 Million 79,731,034 2. 4160919394 1,315,562,176,500,000
34 Million 82,145,364 2. 4160401176 1,396,471,307,000,000
35 Million 84,563,227 2. 4160922000 1,479,856,595,000,000
36 Million 86,979,674 2. 4161020556 1,565,634,258,000,000
37 Million 89,397,247 2. 4161418108 1,653,849,199,000,000
38 Million 91,812,894 2. 4161287895 1,744,445,119,000,000
39 Million 94,228,899 2. 4161256154 1,837,463,667,000,000
40 Million 96,645,213 2. 4161303250 1,932,904,400,000,000
41 Million 99,061,141 2. 4161253902 2,030,753,534,000,000
42 Million 101,476,346 2. 4161034762 2,131,003,413,000,000
43 Million 103,893,138 2. 4161194884 2,233,702,617,500,000
44 Million 106,309,010 2. 4161138636 2,338,798,374,000,000
45 Million 108,723,539 2. 4160786444 2,446,279,785,000,000
46 Million 111,138,308 2. 4160501739 2,556,181,245,000,000
47 Million 113,554,695 2. 4160573404 2,668,535,497,000,000
48 Million 115,969,543 2. 4160321458 2,783,269,200,000,000
49 Million 118,387,016 2. 4160615510 2,900,482,063,500,000
50 Million 120,802,305 2. 4160461000 3,020,057,800,000,000
51 Million 123,218,044 2. 4160400784 3,142,060,300,500,000
52 Million 125,634,154 2. 4160414231 3,266,488,186,000,000
53 Million 128,050,160 2. 4160407547 3,393,329,425,500,000
54 Million 130,463,975 2. 4159995370 3,522,527,514,000,000
55 Million 132,880,223 2. 4160040545 3,654,206,325,000,000
56 Million 135,295,252 2. 4159866429 3,788,267,252,000,000
57 Million 137,712,060 2. 4160010526 3,924,793,909,500,000
58 Million 140,128,242 2. 4160041724 4,063,719,221,000,000
59 Million 142,544,153 2. 4160025932 4,205,052,720,000,000
60 Million 144,958,406 2. 4159734333 4,348,752,390,000,000
61 Million 147,375,122 2. 4159856066 4,494,941,434,500,000
62 Million 149,790,895 2. 4159821774 4,643,517,962,000,000
63 Million 152,207,835 2. 4159973810 4,794,547,023,000,000
64 Million 154,623,289 2. 4159888906 4,947,945,472,000,000
65 Million 157,038,002 2. 4159692615 5,103,735,292,500,000
66 Million 159,455,103 2. 4159864091 5,262,018,630,000,000
67 Million 161,871,411 2. 4159912090 5,422,692,503,000,000
68 Million 164,287,044 2. 4159859412 5,585,759,734,000,000
69 Million 166,704,687 2. 4160099565 5,751,311,943,000,000
70 Million 169,121,766 2. 4160252286 5,919,262,055,000,000
71 Million 171,538,507 2. 4160353099 6,089,617,247,000,000
72 Million 173,953,453 2. 4160201806 6,262,324,560,000,000
73 Million 176,368,856 2. 4160117260 6,437,463,499,500,000
74 Million 178,784,747 2. 4160100946 6,615,035,898,000,000
75 Million 181,199,797 2. 4159972933 6,794,992,650,000,000
76 Million 183,616,094 2. 4160012368 6,977,411,838,000,000
77 Million 186,032,643 2. 4160083506 7,162,257,025,000,000
78 Million 188,447,228 2. 4159901026 7,349,442,165,000,000
79 Million 190,862,368 2. 4159793418 7,539,063,812,500,000
80 Million 193,277,613 2. 4159701625 7,731,104,800,000,000
81 Million 195,693,825 2. 4159731481 7,925,600,196,000,000
82 Million 198,109,015 2. 4159635976 8,122,469,902,000,000
83 Million 200,524,477 2. 4159575542 8,321,766,086,000,000
84 Million 202,939,323 2. 4159443214 8,523,451,860,000,000
85 Million 205,355,672 2. 4159490824 8,727,616,357,500,000
86 Million 207,771,197 2. 4159441512 8,934,161,772,000,000
87 Million 210,186,316 2. 4159346667 9,143,105,050,500,000
88 Million 212,602,940 2. 4159425000 9,354,529,668,000,000
89 Million 215,018,872 2. 4159423820 9,568,340,115,500,000
90 Million 217,433,686 2. 4159298444 9,784,516,185,000,000
91 Million 219,850,418 2. 4159386593 10,003,194,337,500,000
92 Million 222,266,315 2. 4159382065 10,224,250,812,000,000
93 Million 224,680,750 2. 4159220430 10,447,655,200,500,000
94 Million 227,095,084 2. 4159051489 10,673,469,277,000,000
95 Million 229,512,704 2. 4159232000 10,901,853,772,500,000
96 Million 231,928,518 2. 4159220625 11,132,569,200,000,000
97 Million 234,344,371 2. 4159213505 11,365,702,333,000,000
98 Million 236,759,404 2. 4159122857 11,601,211,139,000,000
99 Million 239,175,318 2. 4159123030 11,839,178,587,500,000
100 Million 241,590,277 2. 4159027700 12,079,514,200,000,000
101 Million 244,006,839 2. 4159092970 12,322,345,723,000,000
102 Million 246,423,282 2. 4159145294 12,567,587,739,000,000
103 Million 248,840,359 2. 4159258155 12,815,278,849,000,000
104 Million 251,254,880 2. 4159123077 13,065,254,124,000,000
105 Million 253,670,404 2. 4159086095 13,317,696,577,500,000
106 Million 256,084,270 2. 4158893396 13,572,466,681,000,000
107 Million 258,498,530 2. 4158741121 13,829,671,729,500,000
108 Million 260,914,435 2. 4158743981 14,089,379,868,000,000
109 Million 263,328,945 2. 4158618807 14,351,427,884,000,000
110 Million 265,745,475 2. 4158679545 14,616,001,510,000,000
111 Million 268,160,697 2. 4158621351 14,882,919,072,000,000
112 Million 270,575,863 2. 4158559196 15,152,248,720,000,000
113 Million 272,991,794 2. 4158565841 15,424,036,756,500,000
114 Million 275,405,890 2. 4158411404 15,698,136,129,000,000
115 Million 277,820,730 2. 4158324348 15,974,692,377,500,000
116 Million 280,236,256 2. 4158297931 16,253,703,254,000,000
117 Million 282,651,618 2. 4158257949 16,535,120,062,500,000
118 Million 285,066,604 2. 4158186780 16,818,930,049,000,000
119 Million 287,481,429 2. 4158103277 17,105,145,442,000,000
120 Million 289,896,907 2. 4158075583 17,393,814,840,000,000
121 Million 292,311,641 2. 4157986860 17,684,854,704,000,000
122 Million 294,727,521 2. 4157993525 17,978,379,208,000,000
123 Million 297,143,533 2. 4158010813 18,274,327,710,000,000
124 Million 299,557,657 2. 4157875565 18,572,575,168,000,000
125 Million 301,974,027 2. 4157922160 18,873,377,125,000,000
126 Million 304,389,137 2. 4157868016 19,176,516,072,000,000
127 Million 306,805,299 2. 4157897559 19,482,136,931,000,000
128 Million 309,221,256 2. 4157910625 19,790,160,832,000,000
129 Million 311,637,141 2. 4157917907 20,100,596,046,000,000
130 Million 314,052,527 2. 4157886692 20,413,414,710,000,000
131 Million 316,468,413 2. 4157894122 20,728,681,510,000,000
132 Million 318,884,030 2. 4157881061 21,046,346,442,000,000
133 Million 321,299,093 2. 4157826541 21,366,390,150,000,000
134 Million 323,715,600 2. 4157880597 21,688,945,669,000,000
135 Million 326,131,076 2. 4157857481 22,013,848,102,500,000
136 Million 328,547,998 2. 4157941029 22,341,264,340,000,000
137 Million 330,963,887 2. 4157947956 22,671,026,739,000,000
138 Million 333,379,370 2. 4157925362 23,003,177,013,000,000
139 Million 335,795,486 2. 4157948633 23,337,786,763,500,000
140 Million 338,210,775 2. 4157912500 23,674,754,740,000,000
141 Million 340,626,948 2. 4157939574 24,014,200,327,500,000
142 Million 343,043,659 2. 4158004155 24,356,100,286,000,000
143 Million 345,459,815 2. 4158029021 24,700,377,273,000,000
144 Million 347,875,673 2. 4158032847 25,047,048,960,000,000
145 Million 350,292,487 2. 4158102552 25,396,205,815,000,000
146 Million 352,708,290 2. 4158102055 25,747,705,681,000,000
147 Million 355,125,177 2. 4158175306 26,101,701,024,000,000
148 Million 357,540,909 2. 4158169527 26,458,027,784,000,000
149 Million 359,956,876 2. 4158179597 26,816,787,783,500,000
150 Million 362,372,813 2. 4158187533 27,177,961,500,000,000
151 Million 364,788,891 2. 4158204702 27,541,561,799,000,000
152 Million 367,204,161 2. 4158168487 27,907,516,768,000,000
153 Million 369,619,640 2. 4158146405 28,275,902,995,500,000
154 Million 372,035,743 2. 4158165130 28,646,752,750,000,000
155 Million 374,450,389 2. 4158089613 29,019,905,690,000,000
156 Million 376,866,208 2. 4158090256 29,395,564,770,000,000
157 Million 379,281,305 2. 4158044904 29,773,582,992,000,000
158 Million 381,697,126 2. 4158045949 30,154,073,507,000,000
159 Million 384,113,355 2. 4158072642 30,537,012,279,000,000
160 Million 386,529,610 2. 4158100625 30,922,369,360,000,000
161 Million 388,944,754 2. 4158059255 31,310,053,260,500,000
162 Million 391,360,944 2. 4158082963 31,700,237,031,000,000
163 Million 393,776,305 2. 4158055521 32,092,769,428,000,000
164 Million 396,192,233 2. 4158062988 32,487,763,680,000,000
165 Million 398,607,648 2. 4158039273 32,885,131,537,500,000
166 Million 401,023,403 2. 4158036325 33,284,943,030,000,000
167 Million 403,439,651 2. 4158062934 33,687,211,443,000,000
168 Million 405,856,956 2. 4158152143 34,091,984,892,000,000
169 Million 408,272,435 2. 4158132249 34,499,021,349,000,000
170 Million 410,688,792 2. 4158164235 34,908,547,915,000,000
171 Million 413,104,065 2. 4158132456 35,320,398,156,000,000
172 Million 415,517,439 2. 4157990640 35,734,500,356,000,000
173 Million 417,933,403 2. 4158000173 36,151,239,965,000,000
174 Million 420,349,873 2. 4158038678 36,570,439,560,000,000
175 Million 422,765,244 2. 4158013943 36,991,959,462,500,000
176 Million 425,181,055 2. 4158014489 37,415,933,456,000,000
177 Million 427,599,027 2. 4158137119 37,842,514,509,000,000
178 Million 430,016,536 2. 4158232360 38,271,472,327,000,000
179 Million 432,433,414 2. 4158291285 38,702,791,179,500,000
180 Million 434,849,911 2. 4158328389 39,136,492,620,000,000
181 Million 437,267,293 2. 4158413978 39,572,690,650,000,000
182 Million 439,682,132 2. 4158358901 40,011,074,649,000,000
183 Million 442,097,346 2. 4158324918 40,451,907,799,500,000
184 Million 444,512,168 2. 4158270000 40,895,120,100,000,000
185 Million 446,927,453 2. 4158240703 41,340,790,050,000,000
186 Million 449,343,164 2. 4158234624 41,788,914,903,000,000
187 Million 449,343,164 2. 4158237594 42,239,471,175,000,000
188 Million 454,174,655 2. 4158226330 42,692,418,228,000,000
189 Million 456,588,593 2. 4158126614 43,147,622,700,000,000
190 Million 459,004,983 2. 4158157000 43,605,474,050,000,000
191 Million 461,419,218 2. 4158074241 44,065,535,987,500,000
192 Million 463,835,090 2. 4158077604 44,528,169,312,000,000
193 Million 466,250,388 2. 4158051192 44,993,163,117,500,000
194 Million 468,667,675 2. 4158127577 45,460,765,154,000,000
195 Million 471,085,391 2. 4158225179 45,930,826,305,000,000
196 Million 473,503,339 2. 4158333622 46,403,327,908,000,000
197 Million 475,919,151 2. 4158332538 46,878,037,063,000,000
198 Million 478,335,425 2. 4158354798 47,355,207,768,000,000
199 Million 480,750,860 2. 4158334673 47,834,711,266,500,000
200 Million 483,166,859 2. 4158342950 48,316,686,600,000,000
201 Million 485,581,911 2. 4158304030 48,800,982,759,000,000
202 Million 487,996,904 2. 4158262574 49,287,688,011,000,000
203 Million 490,413,021 2. 4158276897 49,776,922,342,000,000
204 Million 492,829,843 2. 4158325637 50,268,644,700,000,000
205 Million 495,245,922 2. 4158337659 50,762,707,722,500,000
206 Million 497,662,056 2. 4158352233 51,259,192,489,000,000
207 Million 500,077,852 2. 4158350338 51,758,058,406,500,000
208 Million 502,495,484 2. 4158436731 52,259,531,064,000,000
209 Million 504,913,664 2. 4158548517 52,763,478,619,500,000
210 Million 507,329,950 2. 4158569048 53,269,645,485,000,000
211 Million 509,745,400 2. 4158549763 53,778,140,438,500,000
212 Million 512,162,233 2. 4158595896 54,289,197,440,000,000
213 Million 514,577,796 2. 4158581972 54,802,536,019,500,000
214 Million 516,992,665 2. 4158535748 55,318,215,904,000,000
215 Million 519,408,582 2. 4158538698 55,836,423,317,500,000
216 Million 521,825,691 2. 4158596806 56,357,175,384,000,000
217 Million 524,242,175 2. 4158625576 56,880,276,747,000,000
218 Million 526,658,409 2. 4158642615 57,405,767,344,000,000
219 Million 529,075,350 2. 4158691781 57,933,751,591,500,000
220 Million 531,491,865 2. 4158721136 58,464,105,920,000,000
221 Million 533,907,350 2. 4158703620 58,996,762,948,500,000
222 Million 536,322,341 2. 4158664009 59,531,780,628,000,000
223 Million 538,737,263 2. 4158621659 60,069,205,605,000,000
224 Million 541,153,446 2. 4158635982 60,609,186,736,000,000
225 Million 543,569,184 2. 4158630400 61,151,533,987,500,000
226 Million 545,986,095 2. 4158676770 61,696,429,526,000,000
227 Million 548,402,519 2. 4158701278 62,243,686,701,000,000
228 Million 550,818,415 2. 4158702412 62,793,300,108,000,000
229 Million 553,233,019 2. 4158647118 63,345,181,477,000,000
230 Million 555,650,203 2. 4158704478 63,899,774,150,000,000
231 Million 558,065,511 2. 4158680130 64,456,567,329,000,000
232 Million 560,480,471 2. 4158640991 65,015,735,448,000,000
233 Million 562,896,706 2. 4158656910 65,577,467,064,500,000
234 Million 565,311,914 2. 4158628803 66,141,494,757,000,000


HINWEIS: Berend Jan van der Zwaag der Niederlande hat darauf aufmerksam gemacht, dass die Palindrome in der nachstehenden Tabelle geprüft werden möglicherweise im Irrtum. Seine Ergebnisse unterscheiden sich von meiner eigenen. Ich bin in sie suchen, und diese zu korrigieren, wie ich herausfinden, wer ist richtig. (Obwohl ich vermute, dass es wahrscheinlich Berend, der ist richtig...)

Unten ist ein paar Daten der Palindrome in einige Dateien von sehr großen Zahlen gefunden. Die meisten der Dateien sind die Ergebnisse dieser 196 Quest, sondern um eine größere Stichprobe haben, entnahm ich, eine gewisse Anzahl von Dateien aus der Bahn. Es ist mir egal, wenn die Berechnungen der Anzahl Dateien korrekt sind, (außer für die 196 Dateien Ich will DIE RICHTIG! :-)) Mein Ziel war es nur sammeln einige sehr große Zahl setzt, und testen sie für Palindrome .

Tabelle Legend

Die "Data Set Basis" ist eine allgemeine Vorstellung von dem, was berechnet wird, um die Anzahl zu finden. Die meisten von ihnen sind meine eigenen 196 Dateien.

"Datei Länge" ist die Anzahl der Stellen in der Datei vom Autor behauptet. Ich habe nicht gezählt die Ziffern in anderer Leute Dateien, so dass ich nur noch darauf vertrauen, dass sie vorsichtig waren.

"File Location" ist, wo ich die Datei gefunden von über das Internet. Auch hier sind die meisten dieser meiner eigenen lokalen Dateien, aber ich eine URL zu denen, die ich kann, aus dem Internet, würde, falls jemand gerne meine Erkenntnisse zu überprüfen. (Das wäre nicht meine Gefühle verletzt !!!)

"# Selbst von Pals" ist, wie viele Palindrome von 6 Ziffern lang oder mehr, die ich gefunden, die eine gerade Anzahl von Ziffern.

haben

"# of Odd Pals" ist, wie viele Palindrome von 7 Ziffern lang oder mehr, die ich gefunden, die eine ungerade Anzahl von Ziffern.

haben

"Prozentsatz" ist der Prozentsatz der findet sogar zu Chancen.

Data Set Basis Datei Länge File Location # Selbst von Pals # von Odd Pals Prozentsatz
SQRT 2 2,000,000 Robert Nemiroff and Jerry Bonnell 948 1,649 57
SQRT 5 1,000,000 Robert Nemiroff and Jerry Bonnell 655 906 72
SQRT 6 1,000,000 Robert Nemiroff and Jerry Bonnell 625 918 68
SQRT 7 1,000,000 Robert Nemiroff and Jerry Bonnell 628 905 69
SQRT 8 1,000,000 Robert Nemiroff and Jerry Bonnell 591 872 67
SQRT 10 1,000,000 Robert Nemiroff and Jerry Bonnell 646 868 74
196 Calc 1,000,000 Local File 722 887 81
196 Calc 2,000,000 Local File 1,033 1,754 59
196 Calc 3,000,000 Local File 1,229 2,401 51
196 Calc 4,000,000 Local File 1,304 3,154 41
196 Calc 5,000,000 Local File 1,559 3,687 42
196 Calc 6,000,000 Local File 1,583 4,334 37
196 Calc 7,000,000 Local File 1,532 4,645 33
196 Calc 8,000,000 Local File 1,669 5,320 31
196 Calc 9,000,000 Local File 1,659 5,643 29
196 Calc 10,000,000 Local File 2,435 6,164 40
196 Calc 11,000,000 Local File 2,134 6,434 33
196 Calc 12,000,000 Local File 2,061 6,928 30
196 Calc 13,000,000 Local File 4,641 6,925 67
196 Calc 14,000,000 Local File 2,098 7,317 29
196 Calc 15,000,000 Local File 2,290 7,925 29
196 Calc 16,000,000 Local File 2,624 7,758 34
196 Calc 17,000,000 Local File 2,660 8,041 33
196 Calc 18,000,000 Local File 2,426 8,702 28
196 Calc 19,000,000 Local File 2,700 8,910 30
196 Calc 20,000,000 Local File 3,036 9,036 34
196 Calc 21,000,000 Local File 2,997 8,945 34
196 Calc 22,000,000 Local File 3,111 9,324 33
196 Calc 23,000,000 Local File 3,219 9,404 34
196 Calc 24,000,000 Local File 2,713 10,028 27
196 Calc 25,000,000 Local File 5,161 10,299 50
196 Calc 26,000,000 Local File 7,266 9,978 73
196 Calc 27,000,000 Local File 2,999 10,631 28
196 Calc 28,000,000 Local File 3,608 10,264 35
196 Calc 29,000,000 Local File 3,773 10,438 36
196 Calc 30,000,000 Local File 3,406 10,550 32
196 Calc 31,000,000 Local File 3,925 10,676 37
196 Calc 32,000,000 Local File 4,054 10,782 38
196 Calc 33,000,000 Local File 3,815 11,218 34
196 Calc 34,000,000 Local File 4,391 11,336 39
196 Calc 35,000,000 Local File 3,548 11,607 31
196 Calc 36,000,000 Local File 4,074 11,650 35
196 Calc 37,000,000 Local File 3,848 11,739 33
196 Calc 38,000,000 Local File 3,814 11,930 32
196 Calc 39,000,000 Local File 4,231 12,005 35
196 Calc 40,000,000 Local File 4,699 11,870 40

Ich finde das sehr interessant! Es gibt die gleiche Anzahl von selbst stellige Palindrome als ungeraden, von hier bis unendlich. Doch in jedem einzelnen Testfall erwähnt, gibt es etwa 3 mal so viele ungerade Ziffer Palindrome als ausgleicht. Auch wenn ich technisch beginnend mit einer härteren suchen, weil es mehr Ziffern werden. (Dies gilt auch für die anderen Datensätzen, dass ich nicht oben aufgeführt haben, sowie...)

Wenn ich den Grund für diese Vermutung hätte, würde ich sagen, dass es mit der Wahrscheinlichkeit des zweistelligen in der Mitte des glättet tun hat.

Richard Farmbrough aus dem Vereinigten Königreich schickte mir folgendes:

Ich interessiere mich für Ihre Anmerkungen zu gerade / ungerade pal-Distributionen.

Ihr vorgeschlagen Grund (zweistellig) ist nicht gültig, weil XX hat die gleiche Wahrscheinlichkeit wie XYX.

(wobei Y = oder <> X sein kann)

In beiden Fällen beträgt 10%.

Rgds,
Richard.

Ich habe nie jemanden gesehen, der Erörterung dieser auf einer der Seiten, die ich gelesen habe. Hat jemand eine Eingabe?