Pick 22: Combinations and Permutations

Reply #17

JADELottery — Tue, 21 Nov 2006 09:50:41 GMT

Also, I've posted this in a different topic at some point in the past. It might help.

PICK_1_TO_PICK_10_BASE_FORM_COMB_PERM_PROD_TOTAL_OCCUR.xls

It's an Excel sheet I've come up with for all combination and permutation related info on Pick 1 to Pick 10.

Reply #16

JADELottery — Tue, 21 Nov 2006 09:42:34 GMT

Well, I'll get to crunchin'... hopefully we are arriving at the same point, but from different directions.

Reply #15

Thoth — Tue, 21 Nov 2006 09:35:06 GMT

Actual I wasn't referring to consecutive repeats. ??

hmm..... maybe I shouldn't use to the word repeat at all because technically one could say a repeat doesn't occur until the digit has already been drawn at least once.

How about Digit Count within total permutations? My goal was to find the exact number of times a particular digit occurred within the total amount of permuations that are possible...effectively giving the exact probability for a particular digit to occur X amount of t... [ More ]

Reply #14

JADELottery — Tue, 21 Nov 2006 09:16:20 GMT

However in the number 1859095435601128890252 there are the following repeated numbers

0 - 3

1 - 3

2 - 3

5 - 4

8 - 3

9 - 3

But they are not all consecutive.

1 and 8 have a consecutive repeat of 11 and 88.

Reply #13

JADELottery — Tue, 21 Nov 2006 09:07:35 GMT

Ah, ok... you are referring to consecutive repetition only and not repetition in general.

Hmmm, makes a little more sense.

Reply #12

Thoth — Tue, 21 Nov 2006 09:04:30 GMT

Jade

Your picking a number between 0 and 9, (thats ten digits to choose from) but your guessing/picking 22 in a row. Like Pick 3 (3 times) or Pick 4 (4 times), but for pick 22 it's 22 times.

The digits could be the same all 22 times:

7777777777777777777777

OR the digit doesn't have to come up at all:

1859095435601128890252 (no 7 in there)

See where I'm coming from

Reply #11

Thoth — Tue, 21 Nov 2006 08:40:48 GMT

Note to readers, the table is digit specific. so these percentages apply to all digits by themselves. For example, the probability to see exactly five digit 7's drawn in position-one within the next 22 pick 3 or pick 4 games is 4.39%. The probability to see exactly six digit 7's is 1.38%, etc.

It's interesting to note that:

It's almost two and a half times more likely to see your digit drawn exactly one time than not at all.The chance that your digit will be drawn exactly two times is be... [ More ]

Reply #10

JADELottery — Tue, 21 Nov 2006 08:02:34 GMT

Here's why. Let's say all the numbers in the first 10 selections are different and just by chance they are:

0123456789

When it comes time to picking the 11th selection, what's left to select?

0123456789? (? is any number 0 through 9)

No matter what number is selected, there will be at a minimum at least 2 matching numbers and no less.

Now extend this to 20 numbers for the minimum of 2 matching, the first 20 selections are:

01234567890123456789

What happens on the 21st sele... [ More ]

Reply #9

JADELottery — Tue, 21 Nov 2006 07:52:32 GMT

Something don't seem right. With 22 numbers, you a guaranteed to have 3 repeating numbers, absolutely, positively. There should be no way to have only 2, 1, or 0 repeating numbers because of repetition with only 10 numbers (0 through 9).

Reply #8

Thoth — Tue, 21 Nov 2006 07:45:14 GMT

Everything adds up perfect! It will be interesting to see what you can come up with for the outcome patterns or Basic Forms.

(n!)/(r!)/((n-r)!)*(9^(n-r))

REPEATSPERMUTATIONSPROBABILITYPERCENTAGE

2210.00000000000000000000010.00000000000000000001

211980.00000000000000000001980.00000000000000000198

2018,7110.00000000000000000187110.00000000000000018711

191,122,6600.0000000000000001122660.000000000000011227

1847,993,7150.00000000000000479937150.00000000000047994

171,5... [ More ]

Reply #7

Thoth — Tue, 21 Nov 2006 02:10:50 GMT

I think I craked it...can't believe an answer so simple eluded me for so long!

I think this should work, provided that N^0=1 and 0!=1.

To get the precise number of permutations that contain exactly X amount of a specified digit:

n = trials or spaces (i.e. Pick 3 = 3, Pick 4 = 4, Pick 22 =22)

r = exact amount of repeated digit (two digits 4,s or three digit 4,s etc...)

(n!)/(r!)/((n-r)!)*(9^(n-r

Reply #6

JADELottery — Mon, 20 Nov 2006 21:01:48 GMT

I think I'm relatively close though.

I have to rework the logic in deducing the counts.

Reply #5

Thoth — Mon, 20 Nov 2006 17:12:52 GMT

LOL!!! Yea, I think I fried a few circuits of my own.

Its pandora's Box...inside another box...inside a box...inside a another box...inside a box...inside another box ...inside..

Reply #4

JADELottery — Mon, 20 Nov 2006 15:22:39 GMT

Nevermind, I'm spending too much time on this.

My mind is turning in to permutational mush.

Reply #3

JADELottery — Mon, 20 Nov 2006 14:57:26 GMT

Here's the basic permutational form count:

N

Base Form Count

3

1

4

177

5

8,290

6

40,928

7

89,517

8

114,837

9

102,525

10

72,875

11

44,889

12

25,185

13

13,262

14

6,662

15

3,110

16

1,288

17

487

18

173

19

58

20

18

21

5

22

1

Total

524,288

Reply #2

JADELottery — Mon, 20 Nov 2006 14:37:56 GMT

I have most of the logic worked out, however, I need to work it into a single formula or combination of formulae.

Here's the Pick 22 sheet I've come up with all the possible permutations for a Pick 22 permutation having N numbers the same.

N

Permutation Count

3

1,185,137,049,600,000

4

2,583,137,881,497,600,000

5

1,410,819,743,342,820,000,000

6

3,554,460,203,427,300,000,000

7

3,214,703,533,042,230,000,000

8

1,371,270,936,447,220... [ More ]

Reply #1

tntea — Sat, 18 Nov 2006 15:02:05 GMT

That was Beautiful.. Thanks.. Lots of work too... Appreciated.

Pick 22: Combinations and Permutations

Thoth — Sat, 18 Nov 2006 08:51:55 GMT

Original Quote by JADELottery: However, when trying to do the work out for Pick 11 there was a computational problem. It had to do with taking 10 numbers 11 at a time. If you think about this, you can see this is impossible. After a few hours, a few beers, and a few nights rest, I realized the solution. The problem has to do with repetition.

I also noticed this problem when I first began listing the patterns for the Pick 22. The solution I came up with was to first not allow duplicates of