" wrote...
Can anyone tell me how to adapt the follwing formula so kindly
provided by Mr. Grove, to enable Excel to generate all the possible
combin(49,4):
...

You really want all 211876 combinations of 4 numbers from 49 numbers without
replacement (i.e., no duplicates)? Results in multiple 4-column ranges all the
way from row 1 down to row 65536?

Far more efficient to use 4 columns.

A1: 1 B1: 2 C1: 3 D1: 4

Then enter the following formulas.

A2: =A1+(B1=47)
B2: =IF(C1<48,B1,IF(B1<47,B1,A2)+1)
C2: =IF(D1<49,C1,IF(C1<48,C1,B2)+1)
D2: =IF(D1<49,D1,C2)+1

F1: =A65536+(B65536=47)
G1: =IF(C65536<48,B65536,IF(B65536<47,B65536,F1)+1)
H1: =IF(D65536<49,C65536,IF(C65536<48,C65536,G1)+1)
I1: =IF(D65536<49,D65536,H1)+1

Select F1:I1, copy, and paste into K1:N1 *and* P1:S1. Don't worry about the
values they show at this point.

Select A2:D2, and fill down into A3:D65536. Then select A2:D65536, copy, and
paste into F2:I65536 and K2:N65536. Select A2:D2, copy, and paste into
P2:S15268.

How you choose to work with this is up to you.

Inaddition can someone provide the most efficient formula that would
enable me to determine the frequency of repetitive quad combinations
in a sample of lottery results.

I have a lottery table with all lottery results in (Columns B:H). The
lottery has 49 balls and 6 balls and the bonus ball are drawn.

B C etc....
1st No 2nd No etc....

Meaning any combination of 4 of the 7 balls in column B through H? That's 35
possible combinations from each row. So, you'd be better off hardcoding all
combinations of (7 choose 4) in another range, namely,

1 2 3 4
1 2 3 5
1 2 3 6
1 2 3 7
1 2 4 5
1 2 4 6
1 2 4 7
1 2 5 6
1 2 5 7
1 2 6 7
1 3 4 5
1 3 4 6
1 3 4 7
1 3 5 6
1 3 5 7
1 3 6 7
1 4 5 6
1 4 5 7
1 4 6 7
1 5 6 7
2 3 4 5
2 3 4 6
2 3 4 7
2 3 5 6
2 3 5 7
2 3 6 7
2 4 5 6
2 4 5 7
2 4 6 7
2 5 6 7
3 4 5 6
3 4 5 7
3 4 6 7
3 5 6 7
4 5 6 7

and call that Comb_7_4. If your range of samples (B2:H99, for example) were
named Samples, then in yet another range, the top-left cell of which I'll name
Quads, generate the combinations of 4 out of 7 using these formulas.

the Quads cell itself:
=INDEX(Samples,1+INT((ROW()-ROW(Quads))/35),
INDEX(Comb_7_4,1+MOD(ROW()-ROW(Quads),35),COLUMN()-COLUMN(Quads)+1))

Fill this right into the next 3 columns. Select this 4-column by 1-row range,
and fill down into the next 3429 rows (this is specific to the number of rows
needed for Samples being B2:H99, i.e., 35 * 98 = 3430).

In the column to the right of this range of formulas enter a formula like (this
one assumes Quads is W2)

4 columns to the right of Quads (AA2 in this example):
=W2&" "&X2&" "&Y2&" "&Z2

and fill this down into the same row as the range of formulas to the left of it.
To the right of that enter another formula.

5 columns to the right of Quads (AB2 in this example):
=COUNTIF($AA$2:$AA$3431,AA2)

and fill this down into the same row as the range of formulas to the left of it.
Then enter dummy field names like A and B in AA1 and AB1, respectively. Select
AA1:AB3431 and run an advanced filter (Data Filter Advanced Filter...),
select 'Copy to another location', check 'Unique records only', and in the 'Copy
to' field select yet another range, and click OK. When the result will be the
4-ball combinations in the left column and the number of times they appeared in
Samples in the right column.

Knowing how to do this stuff is possibly valuable. Spending time doing this sort
of stuff to play lotteries is a monumental waste of time. Find the most frequent
'quad' in the first half of your samples, then see how often it appears in the
second half. Note: if you're thinking about playing the most frequent 'quad'
along with all other combinations of 2 numbers, be aware that that'd require 990
sets of numbers (45 choose 2 = 45 * 44 / 2). Your odds of winning by doing this
would be slightly worse than 1 out of 14,125.

--
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Dearest Mr. Grove,

I am eternally grateful for all your assistance and i'm humbly working
through your latest formulae.

As a senior contributor who views my endeavors as absurd and futile,
when I hit the Big-one, can I presume you will be presented with an
ethical dilemma on whether or not to forgo your 10% commission? ;)

Thanks once again.

Samuel.

Please remove obvious spam trap if u wish to reply by email.

" wrote...
...
As a senior contributor who views my endeavors as absurd and futile,
when I hit the Big-one, can I presume you will be presented with an
ethical dilemma on whether or not to forgo your 10% commission? ;)
...

Tell ya what, put 1% of your lottery spending into an escrow account for my
benefit. If you bankrupt yourself before winning the big one, I get the money.
If you do win, you get it. Certainly someone with such accumen as you possess
could see such a gamble is virtually a guaranteed winner for you.

Lightning strikes people all the time, and not because they consciously chose to
stand in the wrong place. Purely fortuitous good things happen too, even to
people who believe they caused their own good fortune.

If lotteries were predictable, there's be very, very few fully employed
mathematicians and statisticians. Consider the logical implications of this.

--
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Did you mean acumen?

Mr Grove, if you're going to post condescending retorts, you should at
least get the spelling right; misspellings tend to throw the reader
off the content.


Samuel.

Please remove obvious spam trap if u wish to reply by email.

misspellings tend to throw the reader
off the content.

Apparently.

Seems to me, Harlan invested some time answering your original question and
provided some sage advice at the end. You are the one that baited him.

In fact, if Harlan correctly interpreted your strategy, you are decreasing
your chances. As an example,

Assume 4 letters A, B, C, D

with 3 letter combinations being chosen in a drawing. The combinatorial
possibilities a

ABC
ABD
ACD
BCD

Assume 3 drawings have been held and the results were
ABD
ACD
ABC

As we know, each combination will, over time be chosen an equal number of
times. Picking a combination containing A, your strategy, would actually
lessen your chances, since 3 successes have already been "consumed."

of course, unless the selection system is flawed, each drawing result is
independent of past experience, but if one believes an infinitesimal gain
can be made, you should do the opposite of the most frequently selected
quad.

--
Regards,
Tom Ogilvy



wrote in message
om...
Did you mean acumen?

Mr Grove, if you're going to post condescending retorts, you should at
least get the spelling right; misspellings tend to throw the reader
off the content.


Samuel.

Please remove obvious spam trap if u wish to reply by email.