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 #6
avatar+26400 
+10

Hello, if you could please answer the bellow question, with a easy to follow method, I would be most grateful

A language has 7 total letters in their alphabet.  S, NO, WM, AN.  Every word in this language adds up to 7 letters. The letters that are together have to stay together in every word (W will always be followed by M) . For example "snonono" and "sssanwm" are words in this language, and "sssmwan" or "sssawmn" are not

How many total words are there in this alphabet ?

 

Is  an + no  = ano and  anno in this alphabet ?

 

If an + no = anno :

 

\(\begin{array}{rcl} 1 && sssssss \\ 2 && sssssno \\ 3 && ssssswm \\ 4 && sssssan \\ 5 && ssssnos \\ 6 && sssswms \\ 7 && ssssans \\ 8 && sssnoss \\ 9 && sssnono \\ 10 && sssnowm \\ 11 && sssnoan \\ 12 && ssswmss \\ 13 && ssswmno \\ 14 && ssswmwm \\ 15 && ssswman \\ 16 && sssanss \\ 17 && sssanno \\ 18 && sssanwm \\ 19 && sssanan \\ 20 && ssnosss \\ 21 && ssnosno \\ 22 && ssnoswm \\ 23 && ssnosan \\ 24 && ssnonos \\ 25 && ssnowms \\ 26 && ssnoans \\ 27 && sswmsss \\ 28 && sswmsno \\ 29 && sswmswm \\ 30 && sswmsan \\ 31 && sswmnos \\ 32 && sswmwms \\ 33 && sswmans \\ 34 && ssansss \\ 35 && ssansno \\ 36 && ssanswm \\ 37 && ssansan \\ 38 && ssannos \\ 39 && ssanwms \\ 40 && ssanans \\ 41 && snossss \\ 42 && snossno \\ 43 && snosswm \\ 44 && snossan \\ 45 && snosnos \\ 46 && snoswms \\ 47 && snosans \\ 48 && snonoss \\ 49 && snonono \\ 50 && snonowm \\ \end{array} \begin{array}{rcl} 51 && snonoan \\ 52 && snowmss \\ 53 && snowmno \\ 54 && snowmwm \\ 55 && snowman \\ 56 && snoanss \\ 57 && snoanno \\ 58 && snoanwm \\ 59 && snoanan \\ 60 && swmssss \\ 61 && swmssno \\ 62 && swmsswm \\ 63 && swmssan \\ 64 && swmsnos \\ 65 && swmswms \\ 66 && swmsans \\ 67 && swmnoss \\ 68 && swmnono \\ 69 && swmnowm \\ 70 && swmnoan \\ 71 && swmwmss \\ 72 && swmwmno \\ 73 && swmwmwm \\ 74 && swmwman \\ 75 && swmanss \\ 76 && swmanno \\ 77 && swmanwm \\ 78 && swmanan \\ 79 && sanssss \\ 80 && sanssno \\ 81 && sansswm \\ 82 && sanssan \\ 83 && sansnos \\ 84 && sanswms \\ 85 && sansans \\ 86 && sannoss \\ 87 && sannono \\ 88 && sannowm \\ 89 && sannoan \\ 90 && sanwmss \\ 91 && sanwmno \\ 92 && sanwmwm \\ 93 && sanwman \\ 94 && sananss \\ 95 && sananno \\ 96 && sananwm \\ 97 && sananan \\ 98 && nosssss \\ 99 && nosssno \\ 100 && nossswm \\ \end{array} \begin{array}{rcl} 101 && nosssan \\ 102 && nossnos \\ 103 && nosswms \\ 104 && nossans \\ 105 && nosnoss \\ 106 && nosnono \\ 107 && nosnowm \\ 108 && nosnoan \\ 109 && noswmss \\ 110 && noswmno \\ 111 && noswmwm \\ 112 && noswman \\ 113 && nosanss \\ 114 && nosanno \\ 115 && nosanwm \\ 116 && nosanan \\ 117 && nonosss \\ 118 && nonosno \\ 119 && nonoswm \\ 120 && nonosan \\ 121 && nononos \\ 122 && nonowms \\ 123 && nonoans \\ 124 && nowmsss \\ 125 && nowmsno \\ 126 && nowmswm \\ 127 && nowmsan \\ 128 && nowmnos \\ 129 && nowmwms \\ 130 && nowmans \\ 131 && noansss \\ 132 && noansno \\ 133 && noanswm \\ 134 && noansan \\ 135 && noannos \\ 136 && noanwms \\ 137 && noanans \\ 138 && wmsssss \\ 139 && wmsssno \\ 140 && wmssswm \\ 141 && wmsssan \\ 142 && wmssnos \\ 143 && wmsswms \\ 144 && wmssans \\ 145 && wmsnoss \\ 146 && wmsnono \\ 147 && wmsnowm \\ 148 && wmsnoan \\ 149 && wmswmss \\ 150 && wmswmno \\ \end{array} \begin{array}{rcl} 151 && wmswmwm \\ 152 && wmswman \\ 153 && wmsanss \\ 154 && wmsanno \\ 155 && wmsanwm \\ 156 && wmsanan \\ 157 && wmnosss \\ 158 && wmnosno \\ 159 && wmnoswm \\ 160 && wmnosan \\ 161 && wmnonos \\ 162 && wmnowms \\ 163 && wmnoans \\ 164 && wmwmsss \\ 165 && wmwmsno \\ 166 && wmwmswm \\ 167 && wmwmsan \\ 168 && wmwmnos \\ 169 && wmwmwms \\ 170 && wmwmans \\ 171 && wmansss \\ 172 && wmansno \\ 173 && wmanswm \\ 174 && wmansan \\ 175 && wmannos \\ 176 && wmanwms \\ 177 && wmanans \\ 178 && ansssss \\ 179 && ansssno \\ 180 && anssswm \\ 181 && ansssan \\ 182 && anssnos \\ 183 && ansswms \\ 184 && anssans \\ 185 && ansnoss \\ 186 && ansnono \\ 187 && ansnowm \\ 188 && ansnoan \\ 189 && answmss \\ 190 && answmno \\ 191 && answmwm \\ 192 && answman \\ 193 && ansanss \\ 194 && ansanno \\ 195 && ansanwm \\ 196 && ansanan \\ 197 && annosss \\ 198 && annosno \\ 199 && annoswm \\ 200 && annosan \\ \end{array} \begin{array}{rcl} 201 && annonos \\ 202 && annowms \\ 203 && annoans \\ 204 && anwmsss \\ 205 && anwmsno \\ 206 && anwmswm \\ 207 && anwmsan \\ 208 && anwmnos \\ 209 && anwmwms \\ 210 && anwmans \\ 211 && anansss \\ 212 && anansno \\ 213 && ananswm \\ 214 && anansan \\ 215 && anannos \\ 216 && ananwms \\ 217 && ananans \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \end{array}\)

 

 

laugh

Dec 18, 2015
 #6
avatar+26400 
+5

Die 9 Stellen-Methode heisst nur so. Die Einheiten können beliebig gewählt werden, auch innerhalb der Rechnung kann man die Einheit wechseln.

 

1. Beispiel In zweier Einheiten weiter zerlegen.

\(\begin{array}{lr} 2008\ 00\ 00\ 09\ 70\ 37\ 57\ 00\ 13\ 14\ 00 \\ (1) & 2008 \\ (2) & 00 \\ (3) & 00 \\ (4) & 09 \\ (5) & 70 \\ (6) & 37 \\ (7) & 57 \\ (8) & 00 \\ (9) & 13 \\ (10)& 14 \\ (11)& 00 \\ \end{array}\\ \begin{array}{lr} (1) &2008 ÷ 97 = 20 \text{ Rest } \mathbf{68} \\ (2) &\mathbf{68} 00 ÷ 97 = 70\text{ Rest } \mathbf{10} \\ (3) &\mathbf{10} 00 ÷ 97 = 10 \text{ Rest } \mathbf{30} \\ (4) &\mathbf{30} 09 ÷ 97 = 31 \text{ Rest } \mathbf{2} \\ (5) &\mathbf{02} 70 ÷ 97 = 2 \text{ Rest } \mathbf{76} \\ (6) &\mathbf{76} 37 ÷ 97 = 78 \text{ Rest } \mathbf{71} \\ (7) &\mathbf{71} 57 ÷ 97 = 73 \text{ Rest } \mathbf{76 } \\ (8) &\mathbf{76} 00 ÷ 97 = 78 \text{ Rest } \mathbf{34} \\ (9) &\mathbf{34} 13 ÷ 97 = 35 \text{ Rest } \mathbf{18 } \\ (10)& \mathbf{18} 14 ÷ 97 = 18 \text{ Rest } \mathbf{68} \\ (11)& \mathbf{68} 00 ÷ 97 = 70 \text{ Rest } \mathbf{10} \\ \end{array}\)

 

II. In Einer Einheiten weiter zerlegen.

\(\begin{array}{lr} 20\ 0\ 8\ 0\ 0\ 0\ 0\ 0\ 9\ 7\ 0\ 3\ 7\ 5\ 7\ 0\ 0\ 1\ 3\ 1\ 4\ 0\ 0\\ ( 1) & 20\\ (2) & 0\\ (3) & 8\\ (4) & 0\\ (5) & 0\\ (6) & 0\\ (7) & 0\\ (8) & 0\\ (9) & 9\\ (10) & 7\\ (11) & 0 \\ (12) & 3\\ (13) & 7\\ (14) & 5\\ (15) & 7\\ (16) & 0\\ (17) & 0\\ (18) & 1\\ (19) & 3\\ (20) & 1\\ (21) & 4 \\ (22) & 0\\ (23) & 0\\ \end{array}\\ \begin{array}{lr} (1) & 20 ÷ 97 = 0 \text{ Rest } \mathbf{20}\\ (2) &\mathbf{20} 0 ÷ 97 = 2 \text{ Rest } \mathbf{6}\\ (3) &\mathbf{ 6} 8 ÷ 97 = 0 \text{ Rest } \mathbf{68}\\ (4) &\mathbf{68} 0 ÷ 97 = 7 \text{ Rest } \mathbf{1}\\ (5) &\mathbf{ 1} 0 ÷ 97 = 0 \text{ Rest } \mathbf{10} \\ (6) &\mathbf{10} 0 ÷ 97 = 1 \text{ Rest } \mathbf{3} \\ (7) &\mathbf{ 3} 0 ÷ 97 = 0 \text{ Rest } \mathbf{30}\\ (8) &\mathbf{30} 0 ÷ 97 = 3 \text{ Rest } \mathbf{9}\\ (9) &\mathbf{ 9} 9 ÷ 97 = 1 \text{ Rest } \mathbf{2}\\ (10) &\mathbf{ 2} 7 ÷ 97 = 0 \text{ Rest } \mathbf{27}\\ (11) &\mathbf{27} 0 ÷ 97 = 2 \text{ Rest } \mathbf{76} \\ (12) &\mathbf{76} 3 ÷ 97 = 7 \text{ Rest } \mathbf{84} \\ (13) &\mathbf{84} 7 ÷ 97 = 8 \text{ Rest } \mathbf{71} \\ (14) &\mathbf{71} 5 ÷ 97 = 7 \text{ Rest } \mathbf{36} \\ (15) &\mathbf{36} 7 ÷ 97 = 3 \text{ Rest } \mathbf{76} \\ (16) &\mathbf{76} 0 ÷ 97 = 7 \text{ Rest } \mathbf{81} \\ (17) &\mathbf{81} 0 ÷ 97 = 8 \text{ Rest } \mathbf{34} \\ (18) &\mathbf{34} 1 ÷ 97 = 3 \text{ Rest } \mathbf{50} \\ (19) &\mathbf{50} 3 ÷ 97 = 5 \text{ Rest } \mathbf{18} \\ (20) &\mathbf{18} 1 ÷ 97 = 1 \text{ Rest } \mathbf{84}\\ (21) &\mathbf{84} 4 ÷ 97 = 8 \text{ Rest } \mathbf{68}\\ (22) &\mathbf{68} 0 ÷ 97 = 7 \text{ Rest } \mathbf{1}\\ (23) &\mathbf{1} 0 ÷ 97 = \text{ Rest } \mathbf{10}\\ \end{array}\)

 

Wie gesagt, man kann auch beliebige Einheiten kombinieren, es funktioniert immer.

 

III. In verschiedene Einheiten weiter zerlegen.

\(\begin{array}{lr} 20080000\ 0\ 9\ 7\ 0\ 3\ 7\ 5\ 7\ 0\ 0\ 131400 \\ (1) & 20080000 \\ (2) & 0\\ (3) & 9 \\ (4) & 7\\ (5) & 0 \\ (6) & 3\\ (7) & 7 \\ (8) & 5\\ (9) & 7 \\ (10) & 0\\ (11) & 0 \\ (12) & 131400 \\ \\ \end{array}\\ \begin{array}{lr} (1) &20080000 ÷ 97 = 207010 \text{ Rest } \mathbf{30} \\ (2) &\mathbf{30} 0 ÷ 97 = 3 \text{ Rest } \mathbf{9}\\ (3) &\mathbf{ 9} 9 ÷ 97 = 1 \text{ Rest } \mathbf{2}\\ (4) &\mathbf{ 2} 7 ÷ 97 = 0 \text{ Rest } \mathbf{27}\\ (5) &\mathbf{27} 0 ÷ 97 = 2 \text{ Rest } \mathbf{76} \\ (6) &\mathbf{76} 3 ÷ 97 = 7 \text{ Rest } \mathbf{84} \\ (7) &\mathbf{84} 7 ÷ 97 = 8 \text{ Rest } \mathbf{71} \\ (8) &\mathbf{71} 5 ÷ 97 = 7 \text{ Rest } \mathbf{36} \\ (9) &\mathbf{36} 7 ÷ 97 = 3 \text{ Rest } \mathbf{76} \\ (10) &\mathbf{76} 0 ÷ 97 = 7 \text{ Rest } \mathbf{81} \\ (11) &\mathbf{81} 0 ÷ 97 = 8 \text{ Rest } \mathbf{34} \\ (12) &\mathbf{34} 131400 ÷ 97 = 351870 \text{ Rest } \mathbf{10} \\ \end{array}\)

 

laugh

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