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charliepatrick
charliepatrick
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Gialmere
November 30th, 2022 at 8:02:38 AM permalink
Itís the same number with different bases. Since 30 is divisible by 3 the number must be. One of these is decimal, since 18 isnít there, it must be 15. This gives 120 and 1111 as the last two and F as a giveaway first!
gordonm888
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gordonm888
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Thanks for this post from:
Gialmere
November 30th, 2022 at 9:54:18 AM permalink
Quote: Gialmere


Complete this series:

10, 11, 12, 13, 14, 15, 16, 17, 21, 23, 30, 33, Ö
link to original post


The sequence is 15 in base 15-n

The remainder of the series is 120, 1111, 111111111111111
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
ThatDonGuy
ThatDonGuy
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Thanks for this post from:
Gialmere
November 30th, 2022 at 4:39:12 PM permalink
Quote: Gialmere

Complete this series:

10, 11, 12, 13, 14, 15, 16, 17, 21, 23, 30, 33, Ö
link to original post



120, and 1111

The original list is 15 in base 15, 14, 13, ..., 4; 120 in base 3 and 1111 in base 2 = 15

If you want to get pedantic, it's not technically complete; although bases 1, 0, and -1 are undefined, 15 in base -2 = 10011, since (-2)^4 + (-2)^1 + (-2)^0 = 16 - 2 + 1 = 15.

Gialmere
Gialmere
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November 30th, 2022 at 5:35:28 PM permalink
Quote: charliepatrick

Itís the same number with different bases. Since 30 is divisible by 3 the number must be. One of these is decimal, since 18 isnít there, it must be 15. This gives 120 and 1111 as the last two and F as a giveaway first!

link to original post


Quote: gordonm888

The sequence is 15 in base 15-n

The remainder of the series is 120, 1111, 111111111111111

link to original post


Quote: ThatDonGuy


120, and 1111

The original list is 15 in base 15, 14, 13, ..., 4; 120 in base 3 and 1111 in base 2 = 15

If you want to get pedantic, it's not technically complete; although bases 1, 0, and -1 are undefined, 15 in base -2 = 10011, since (-2)^4 + (-2)^1 + (-2)^0 = 16 - 2 + 1 = 15.


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Correct!!

Well done.
-------------------------------------------

Because Oct 31 = Dec 25

Have you tried 22 tonight? I said 22.
Wizard
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Wizard 
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November 30th, 2022 at 8:18:38 PM permalink
How many unique five-card stud hands are there in a five-deck shoe?

Revised wording: How many distinct combinations of five cards can be made from a five-deck shoe of cards?
Last edited by: Wizard on Dec 1, 2022
ďExtraordinary claims require extraordinary evidence.Ē -- Carl Sagan
gordonm888
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gordonm888
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November 30th, 2022 at 9:17:20 PM permalink
Quote: Wizard

How many unique five-card stud hands are there in a five-deck shoe?
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I think the wording is unclear.

Is this: how many distinct 5 card stud hands can be created from 5 decks of cards?

Or:

Is this: given five decks of cards are shuffled and arranged in a shoe, how many unique 5 card stud hands exist as five consecutive cards in the stack?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
aceside
aceside
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November 30th, 2022 at 9:20:19 PM permalink
I think there is no such a game in the world using a 5-deck shoe for 5-card stud games.
Wizard
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Wizard 
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December 1st, 2022 at 3:07:45 AM permalink
Quote: gordonm888

how many distinct 5 card stud hands can be created from 5 decks of cards?
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That wording is good.

Revised reply: Please do not think about poker. Rather refer to this revised wording, "How many distinct combinations of five cards can be made from a five-deck shoe of cards?"
Last edited by: Wizard on Dec 1, 2022
ďExtraordinary claims require extraordinary evidence.Ē -- Carl Sagan
gordonm888
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gordonm888
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December 1st, 2022 at 6:42:03 AM permalink
As I approached this problem, I wondered why this was in a thread titled Easy Math Problems. Then, as I worked the first hand categories I found its simplicity.


5 singletons (includes straights, straight flushes and unpaired flushes)
c(13,5) *45 =1,317,888

1 pair + 3 singletons (includes flushes with 1 pair)
c(13,4)* 45 =732,160

2 pair + 1 singleton (includes flushes with 2 pair)
c(13,3)* 45 = 292,864

3oak +2 singletons (includes flushes with 3oak)
c(13,3)* 45 = 292,864

3oak + 2oak (includes flushes with full houses)
c(13,2)* 45 = 79,872

4oak + 1 singleton (includes flushes with quads)
c(13,2)* 45 = 79,872

5oak (includes flushes with 5oak)
c(13,1)* 45 = 13,312

Summing up the above numbers gives: 2,808,832
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
aceside
aceside
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December 1st, 2022 at 7:02:06 AM permalink
Itís not clear if a suited 5-of-a-kind hand and an offsuit one are counted as the same rank or not. If yes, there are only 13 different 5-of-a-kind hands.

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