Wikipedia:Reference desk/Archives/Mathematics/2013 January 18

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January 18

Blackjack

Playing blackjack. Blackjack pays 3:2. I have $200, bet $20, and get a blackjack. I get $50 back right? So I now have a total of $230. 86.45.191.101 (talk) 08:34, 18 January 2013 (UTC)

Sounds good, although this assumes you haven't bought insurance. StuRat (talk) 08:54, 18 January 2013 (UTC)

number of subgroups

how to find all subgroups of a finite group — Preceding unsigned comment added by 182.187.2.101 (talk) 09:09, 18 January 2013 (UTC)

There are $2^{n}$ subsets of any finite set of n objects. If that is what you were looking for, I found the Power Set article most useful.--Gilderien Chat|List of good deeds 17:57, 18 January 2013 (UTC)

Most subsets of a group are not subgroups. To the OP, it’s hard to give a sensible answer without further details on what you are trying to do. Do you want to find them by hand or do you need a computer algorithm? Are the groups given by table, presentation, or something else? How large are they? One obvious way is to start with the trivial subgroup, and then for each subgroup H already found, and each element g outside the subgroup, add g to H, and close it under multiplication to get another subgroup. When you cannot generate any more subgroups in this way, you’ve got all of them.—Emil J. 18:21, 18 January 2013 (UTC)

Visual Multiplication with Lines

What is this method of multiplication called and/or do we have an article about it? I couldn't find anything under multiplication.--Shantavira|^{feed me} 13:44, 18 January 2013 (UTC)

I don't see anything special about it other than maybe it is designed to help kids who might be more graphical in the way that they see the world. It's just a visual version of the standard multiplication.Naraht (talk) 14:36, 18 January 2013 (UTC)

The method reminds me of Lattice multiplication, but it's much more visual than that. I was sad to see it isn't listed in Multiplication algorithm - perhaps one to add. 80.195.151.245 (talk) 15:40, 18 January 2013 (UTC)

At second glance, it's more similar to Grid method multiplication than Lattice. 80.195.151.245 (talk) 15:41, 18 January 2013 (UTC)

Amount of starter positions possible in those random chess variants.

What are the amount of starter positions possible in those random chess variants?

A=1-Pawns start at second rank. 2-King start at file d or e. 3- First rook start at file a, b, g, or h but need to be at least 3 squares to the left of right side of the king. 4- Second rook start at other side of the board at file a, b, g, or h but need to be at least 3 squares to the left of right side of the king. 5-Other pieces start at random places in their first rank. 6- No need to players mirror each other.

B=1-Like A but. Players mirror each other.

C=1-Pawns start at second rank. 2-King start at file d or e. 3- First rook start at file a, b, g, or h but need to be at least 3 squares to the left of right side of the king. 4- Second rook start at other side of the board at file a, b, g, or h but need to be at least 3 squares to the left of right side of the king. 6-Other pieces start anywhere. 6.1-They can start at position that check and mate other pieces. — Preceding unsigned comment added by 187.115.239.163 (talk) 15:54, 18 January 2013 (UTC)

For A & B, the number of choices for A is the square of the choices in B. For B, the easiest way is to enumerate for one color the number of K,R&R setup possibilities, which I think are a,d,g; a,d,h; a,e,h; b,e,h. Then the Q,B&N combinations can be done in 30 different ways (5!/(2!*2!)) for a production of 120 for White. This means for A it is 14400 since they are independent. For C, take the original 4 for each side which means 16 possible setups for WK,WR,WR,BK,BR&BR and then the 10 other pieces are scattered over the other 58 squares of the board with is 58!/(2!*2!*2!*2!*48!) (two indist. WN,two indist WB, two indist BN, two indist BB and 48 indist empty squares) so the final results 16* 58!/(2!*2!*2!*2!*48!) which becomes 58!/48! which is 189,348,905,569,824,000.