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Subject: Game quiz: 244,432,188,000 rss

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Mike K
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Simple question: who can identify the gaming significance of the number in the subject heading?

(I don't have any GG to spare; I'm saving up to help my wife get her avatar. With any luck, bragging rights will suffice.)

That number again: 244,432,188,000. As in, Two hundred forty-four billion, four hundred thirty-two million, one hundred eighty-eight thousand.
 
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Pete Belli
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The number of times Busen Memo has been mentioned on BGG?
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Phil Alberg
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Coyotek4 wrote:
Simple question: who can identify the gaming significance of the number in the subject heading?

(I don't have any GG to spare; I'm saving up to help my wife get her avatar. With any luck, bragging rights will suffice.)

That number again: 244,432,188,000. As in, Two hundred forty-four billion, four hundred thirty-two million, one hundred eighty-eight thousand.

I think that's the number of times Joe Huber has played Race for the Galaxy so far this year.

http://www.boardgamegeek.com/thread/295891
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Bill Hice
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Possible configurations of a Settlers game.
 
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Tommy Dean
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Didn't somebody just count all their bits? That number sounds about right IIRC.
 
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Mike K
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gibsonc22 wrote:
Possible configurations of a Settlers game.

Dammit, I didn't think anyone would get it that fast!

Well done.
 
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thomas coe
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the internet is amazing!!! i found the answer just by googling the number. granted, i didn't answer first...but i was right
 
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Mike K
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THORBOY wrote:
the internet is amazing!!! i found the answer just by googling the number. granted, i didn't answer first...but i was right

[Homer] Stupid Flanders Google [/Homer]

(I forgot to include the harbors.)

Guess I'll have to check my answers to see that they're not online.
 
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thomas coe
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hahahahh....NEVER FORGET ABOUT THE INTERNET!!!!!!!
 
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David Molnar
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Of course, like everything else on the internet, it's wrong.
 
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Richard Irving
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THORBOY wrote:
the internet is amazing!!! i found the answer just by googling the number. granted, i didn't answer first...but i was right


Unfortunately, the answer is WRONG, because it does not take into rotational symmetries.


The CORRECT ANSWER is "How many ways can you stack the 19 Settlers land tiles?"

The formaula:
19! / ((4!)^3 * (3!)^2) = 244,432,188,000
is simply the number of permutations that the 19 tiles can be stacked, there are rotational symmetries not accounted for:

But these two set ups are the same--they are just rotated by 60 degrees:

W P
D P W D
P M R F F W
F F P M
W W P W W P
P R R F
F R W M R R
W M M P
M W


(P)asture, (M)ountain, (R)iver, (F)arm, (W)oods, (D)esert

It ALSO doesn't include different positions for the ports and different positions for the numbers--which is just as important in setting a Settlers of Catan Board.

To calculate that, we'll fix the order of tiles with the order and direction of rotation of the numbers as clockwise (I.e. the Top hex will always get number chip A--and the number tiles will be roitated clockwise, skipping the desert) This differentiates the rotational symmetries of the land pieces and sets the total number of land/chip only set ups to the same as original answer: 244,432,188,000.

But there are 9 port tiles, which are setup independently of the land tiles. There are 9 total port tiles: 4 generic 3:1, 5 specific 2:1. The number of permutations is: 9!/4! = 15,120 permutations.

However this is doubled because there are two possible ways to set up the ports: 1 port adjacent the stationary Hex A or 2 ports adjacent to A:

1
2 2
1 A 1
2 * * 2
* * *
1 * * 1
* * *
2 * * 2
* * *
1 * * 1
2 * 2
1 1
2


The actual number of Settlers of Catan Boards, therefore, is:
244,432,188,000 * 2 * 15,120 = 7,391,629,365,120,000


POST EDITED TO CORRECT A NUMERICAL ERROR--there are 4 3:1 ports in the 4 player, not Five. Calculation corrected.
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Laurence Parsons
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rri1 wrote:
The actual number of Settlers of Catan Boards, therefore, is:
244,432,188,000 * 2 * 3024 = 1,478,325,873,024,000

I have to ask - what about with the 5-6 player expansion?
The board is no longer rotationally symetrical in the same way; there are 2 deserts, to upset the way the number tiles are positioned; and there are 2 sheep ports.
 
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Mike K
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rri1 wrote:
THORBOY wrote:
the internet is amazing!!! i found the answer just by googling the number. granted, i didn't answer first...but i was right


Unfortunately, the answer is WRONG, because it does not take into rotational symmetries.


The CORRECT ANSWER is "How many ways can you stack the 19 Settlers land tiles?"

The formaula:
19! / ((4!)^3 * (3!)^2) = 244,432,188,000
is simply the number of permutations that the 19 tiles can be stacked, there are rotational symmetries not accounted for:

Actually, I took the rotational symmetries into account; the thing is:

(1) only the 'reflections' (i.e., placing the chits around the board in the other direction) would result in different-looking boards.

(2) reflections of each other would result in a mirror-image that plays exactly the same way (assuming the dice and cards played out the same way).

I was going for the number of different-playing boards. Yes, I should have been more specific.
 
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Bill Hice
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Thanks
 
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Meng Tan
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You mean that's how many times I have to play Settlers in order to truly master the game?
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Richard Irving
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freduk wrote:
rri1 wrote:
The actual number of Settlers of Catan Boards, therefore, is:
244,432,188,000 * 2 * 3024 = 1,478,325,873,024,000

I have to ask - what about with the 5-6 player expansion? The board is no longer rotationally symetrical in the same way; there are 2 deserts, to upset the way the number tiles are positioned; and there are 2 sheep ports.


The fact of 2 deserts and 2 Sheep Ports, does nothing to affect the handling of rotational symmetry--you only have to account for them when calculating permutations of land and sea tiles. Since the desert ALWAYS forces a skip in the number chip ordering in exactly the same way--adding a second one does not affect the method.

What DOES affect it though is the rules are NOT clear on which corner you start number chip A: There are 3 possibilities all distinct:

1
* *
* * *
2 * * 3
* * *
* * * *
* * *
3 * * 2
* * *
* *
1


If A is at position 1, the first three sides you place number tiles has 4 tiles, then 3, then 4. Position 2: 4,4,3. Position 3: 3,4,4.

But whichever one is picked fixes the possible symmetries (There are only 2--180 degrees apart, rather than 6 on the original 4 player board.

Going through the math:
The Permutation of Land Tiles: 30!/(6!^3 * 5!^2 * 2!) = 24,675,735,016,607,875,200
Times the Permutation of Sea Tiles: 11!/(5! * 2!) = 166,320
Times 3 for different possibilities of where to start number chip A.
Times 2 for the different patterns of port tiles

Equals: 24,624,409,487,773,330,819,584,000
 
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Richard Irving
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Coyotek4 wrote:
rri1 wrote:
THORBOY wrote:
the internet is amazing!!! i found the answer just by googling the number. granted, i didn't answer first...but i was right


Unfortunately, the answer is WRONG, because it does not take into rotational symmetries.


The CORRECT ANSWER is "How many ways can you stack the 19 Settlers land tiles?"

The formaula:
19! / ((4!)^3 * (3!)^2) = 244,432,188,000
is simply the number of permutations that the 19 tiles can be stacked, there are rotational symmetries not accounted for:

Actually, I took the rotational symmetries into account; the thing is:

(1) only the 'reflections' (i.e., placing the chits around the board in the other direction) would result in different-looking boards.

(2) reflections of each other would result in a mirror-image that plays exactly the same way (assuming the dice and cards played out the same way).

I was going for the number of different-playing boards. Yes, I should have been more specific.


You are STILL wrong, because you forgot ports entirely, which produces different playing boards. Having a Mountain port adjacent to a Mountain Hex with a 6 or 8 on it is not the same PLAYING board as having the Mountain port on the other far way from any Mountain hex.
 
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Mike K
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rri1 wrote:
You are STILL wrong, because you forgot ports entirely ...

I mentioned as much above.
 
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