Expert: Ahmed Salami - 11/7/2004

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The U.K.Lottery has 49 numbers we have to choose 6 to win the big prize which makes odds of 13,983,816/1. the lowest possible sum total of six numbers is 21, the highest 279. making 259 different sum totals in all.
So the question is how many combinations are they in each different sum total, I know that the sum total of 150 must hold the most, but how do I find its total combinations?
I'm trying to make the lottery a little bit more controlable and interesting as an alternative to plain guessing
Answer -
Hi bertie,
I'm terribly sorry about the delay.
But i'm afraid i don't really get the question. I'm talking about the different sum total part. I really don't get it. You would do well in writing me back and explaining better.
You'll get a quick response this time.
Regards.

Sorry! Ahmed, I'll try again,
Thanks a lot for replying, but this thing is driving me nuts!
O/k, The lowest possible sum total of 6 numbers must be
1+2+3+4+5+6 = 21 which is just one combination
the highest possible S/T, also holding just one combination must be
44+45+46+47+48+49 = 279 (any 6 from 1 to 49)
From the s/t of 21 to the s/t of 279 there are 259 different s/t's
holding 13,983,816 combinations (279-21 = 258 +1 =259)
Therefore, how many combinations are there if the winning 6 numbers add-up to 150, which also happens to be exactly half way between 21 and 279
(258/2 = 129 + 21 =150, or 279-129 =150)so there must be 129 sum totals on each side of the centre of 150, going from the maximum set of combinations to the minimum on ether side (from 1@21 to max@150? to 1@279)
If my choosen 6 numbers also came to 150, then how close am I to winning the lottery?
To give myself some idea I divided 130 into 13,983,816 for the 150 mark, but this is a straight line graph and must be wrong, anyway it will not help if I wanted say, the sum total of 100 for 6 numbers, which will also have the same amount of combinations as the sum total of 200 etc.,
Hope I hav'nt gone on too long and everything you need is here, don't get too bored will you, and good luck
Thanks again
Kind regards bertie
Must go now and check for this weeks lottery of £18m ,If I have won then you can have a nice holiday on me!!!!:-)bye

Answer -
Hi bertie,
I was about sending you a reply, but i just got another idea. I have to take some time to review it.
I'm sorry to take all the time.
Good luck.

Hi Ahmed
It's bertie again, I only asking if there's any progess on my questions, hope everything is O/K with you. kind regards Bertie
Answer -
Hello bertie,
Been long. I have to confess that i completely forgot about making any progress as regards your question when you gave me the time to. But since you've asked again, i knew it was time i did something about it.
I wouldn't lie to you but i didn't seem to find a direct formula that gives the number of combinations for a particular sum total. Using some intrinsic knowledge, i tried formulating the normal distribution, error function in order to get what i could call a good approximation. Anyway, i ended up using the binomial distribution for the modelling but i'll spare you the maths and go straight. As you already know the nature of the problem, the number of combinations for a sum total of 150 is the greatest.
At the end of my manipulations, i got close to a probability of (258C129)/(2^258)for the sum total of 150.
nCr is read 'n combination r'. This amounts to a probability of about 0.0496 which means that there are about 693961 different combinations to obtain a sum total of 150. I'm hoping i could also use this method for other sum totals too.
Well, as usual, i welcome any additional things you have to say. Forgive me for any delay i've made.
As for your other question about me being OK, i'm not and i haven't been. I always believe that a problem shared is already half solved, we could talk if you want to know, maybe you could have a few inspirational words to say. The truth is that i never underestimate anyone.
Most importantly, i hope i have helped you.
Good luck.
Regards.
Hi Ahmed
Very sorry to hear you have some personal problems talk to me as much as you want if it helps then it's the least I can do for all the trouble I've caused. Thanks for trying but I do feel the answer you gave is a little on the high side, because of the simple straight line graph I first made which gave the 150 sum total holding only 126,780 combinations,which I feel, at best is only about 50% out, you could be right I just don't know, but someone told me about a lottery web site in Canada that may help, have yet to give it a try.
Anyway do come back to me and lets see if I can help! True Regards bertie  


Answer -
Hi Bertie,
How've you been?
I was just wondering why i haven't heard from you.
Take care.
Hi Ahmed
Sorry for the delay but I've been waiting for you to come back to me because my computer crashed and I lost everything, I mean everything. I thought I was protected but the one year firewall run out and they never notified to renew, so bang it went, My computer installer said it was the worst crash he'd seen, it had to me eh!
Anyway I manage to get the combinations for each of 259 sum totals from a Canadian site (I crashed soon after, strange?) The 150 shows it holds 165,772 combinations, but I still don't know how! Perhaps you might be able to workout a formula from this list.
How are you anyway I think you was having problems the last time I e-mailed, hope it's sorted out bye now because time is about the most inexpensive healer you can find apart from keeping busy and friends.
Regards bertie ( who's scared to punch in a key at the moment, it will pass, I hope!)Sorry I dont know how to format so start at the bottom at the 150 mark and the sum of 21 and 279 = 1 comb   


Sum   comb's   Sum
21   1   279
22   1   278
23   2   277
24   3   276
25   5   275
26   7   274
27   11   273
28   14   272
29   20   271
30   26   270
31   35   269
32   44   268
33   58   267
34   71   266
35   90   265
36   110   264
37   136   263
38   163   262
39   199   261
40   235   260
41   282   259
42   331   258
43   391   257
44   454   256
45   532   255
46   612   254
47   709   253
48   811   252
49   931   251
50   1,057   250
51   1,206   249
52   1,360   248
53   1,540   247
54   1,729   246
55   1,945   245
56   2,172   244
57   2,432   243
58   2,709   242
59   3,009   241
60   3,331   240
61   3,692   239
62   4,070   238
63   4,494   237
64   4,935   236
65   5,426   235
66   5,940   234
67   6,506   233
68   7,079   232
69   7,748   231
70   8,423   230
71   9,163   229
72   9,933   228
73   10,769   227
74   11,637   226
75   12,579   225
76   13,552   224
77   14,603   223
78   15,690   222
79   16,856   221
80   18,059   220
81   19,349   219
82   20,673   218
83   22,087   217
84   23,940   216
85   25,082   215
86   26,663   214
87   28,340   213
88   30,051   212
89   31,860   211
90   33,706   210
91   35,648   209
92   37,625   208
93   39,703   207
94   41,809   206
95   44,016   205
96   46,253   204
97   48,586   203
98   50,944   202
99   53,402   201
100   55,875   200
101   58,446   199
102   61,031   198
103   63,706   197
104   66,388   196
105   69,161   195
106   71,928   194
107   74,781   193
108   77,624   192
109   80,542   191
110   83,440   190
111   86,412   189
112   89,348   188
113   92,340   187
114   95,311   186
115   98,324   185
116   101,285   184
117   104,295   183
118   107,235   182
119   110,215   181
120   113,119   180
121   116,048   179
122   118,889   178
123   121,751   177
124   124,507   176
125   127,274   175
126   129,930   174
127   132,581   173
128   135,109   172
129   137,629   171
130   140,008   170
131   142,370   169
132   144,587   168
133   146,771   167
134   148,800   166
135   150,794   165
136   152,627   164
137   154,397   163
138   156,004   162
139   157,554   161
140   158,923   160
141   160,236   159
142   161,354   158
143   162,410   157
144   163,273   156
145   164,062   155
146   164,654   154
147   165,176   153
148   165,490   152
149   165,732   151
150   165,772   150


Answer
Hi Bertie,
Thank you for the reply.
I'm sorry about your computer, hope you've had it sorted out now.
About what i wanted to share with you, i'm not sure it would be convenient on here. If you don't mind, we could talk via email or even instant messaging on yahoo or msn. Just let me know whichever one suits you most even if it is on here.
Thank you for the concern, i really want to share this.
I await your quick response. Take care.
Regards.