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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 ?

 Dec 17, 2015

Best Answer 

 #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
 #1
avatar+33665 
0

There are 4 groups of letters, so there are 4! = 24 possible words.  This assumes there are no repeats.

 

Edited to correct from 5 to 4 groups (I obviously can't count!).

 

But repeats seem to be allowed, so more thought required!

 Dec 17, 2015
edited by Alan  Dec 17, 2015
edited by Alan  Dec 17, 2015
 #2
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0

But there are not 5 groups of letters because some combinations go over 7 letters. Also there are 4 groups of letters. That didnt answer the quastion

 Dec 17, 2015
 #3
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0

Alan: He seems to allow "repeats" Will it be different?

 Dec 17, 2015
 #4
avatar+8581 
0

These are always so tricky!

 Dec 17, 2015
 #5
avatar+33665 
+5

Ok.  I think these are the possibilities:

 

words

.

 Dec 17, 2015
 #6
avatar+26400 
+10
Best Answer

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

heureka Dec 18, 2015

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