# anybody good in theorycrafting mathematic?

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#### yvon_la

ok if i got 3 different value what would be the theoretical total amount of possibility ?never having the same whatever twice.you can d o whatever you want with those tree value as long as the result is different and it only use those tree value then that possibility is valid ! what would be the total number of theoretical possibility? i think its 9 !but i didnt go to school long enough so i aint sure

#### Geauxtiger

I think this is what you are asking: 3 digit number. Each digit can only be used once. First digit can be any digit from 0-9, meaning there are 10 choices. The second digit has only 9 choices since there cannot be a repeat of the 1st digit above. The 3rd digit has only 8 choices since 2 of have already been used for the 1st and 2nd digit. So, the total possible combination of digits is 10*9*8 = 720 There are 270 possible 3 digit number combinations that do not have a repeating digit.

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#### yvon_la

nonono! it isnt 0 to 9 call them say x y z if you must have a name .that is it , nothing else there is no number letter etc ! it can only be x or y or z or combination of those three . x is different then y and y is different then z etc etc but that is it!

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#### yvon_la

ok i aint sure i explained right ,because iwas looking at mathematic and almost everything i write means something else in mathematic i just want to know the total amount of posssible result if you have only 3 known! yes i think this define it better

#### Geauxtiger

Is the number 123 an example of the xyz you are talking about? If so, then I think my explanation above is correct. If these 3 values are alphabet letters, then the possible combinations are 26*25*24= 15,600 letter combinations or a 1 in 15,600 chance of selecting any given 3 letter combo.

#### yvon_la

no my last post explain it better if you got 3 known how many different result can we come up with no number no nothing if you only know 3 value but you dont know what the value are how many result can you come up with ( knowing that you dont know what the value is)

#### bprimerano

If you always include all three and are interested in the possible combinations, its 6. XYZ XZY YXZ YZX ZXY ZYX. If you want combinations that do not include all three and order is not important there are 8. X Y Z XY XZ YZ XYZ and none.

#### Brian Barnhart

If I understand correctly, the answer is 6 The first digit can be any one of three The second digit can be any one of the remaining two The last one is the remaining one 3 X 2 X 1 = 6 xyz xzy yxz yzx zxy zyx Edit: Oops, too slow...

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#### yvon_la

ok! i dont understand the last answer but i think you got the right of it !your first answer is the way i thing it works why 6 how come not 9?( like a when you play tictactoc you got 9 case if you put one xyz on top and xyz vertically you get 9 result no? i ask because i was expecting the total amount of different conbination of 3 different value to be 9 . i reworded because you made me think of another condition. i dont think can be a non combination . i think it has to be a different combination with this what would the answer be? sorry i am finding out i know very little about math and forgot there are a lot of things to mention i take for granted but i didnt specify sorry

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#### yvon_la

xyz x123 y456 z789 so this would end up with 9 possibility right?

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#### mk378

On a tic tac toe board there are only two choices X and O but they can be reused, so there are 2 * 2 * 2 ways to fill out a line of 3, the answer is 8. Now for filling out the whole board, you would have to look at the 2 ^ 9 (512) possible ways to fill a board and exclude all that don't have 5 X's and 4 O's (since X goes first he plays 5 turns and O plays 4, unless someone wins) Also you may want to exclude rotational variants of the same game.

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#### yvon_la

ok imagine (i know it isnt real but i am trying to know something and there is always a detail i forget ( like now you included the tic tac toe game rule ) when it does not apply the tictactoe board is only there because its conviniant so if 3*3*3 ways to fill out a line of 3 the answer would be 9 right?

3*3*3=27 not 9.

#### JimPghPA

yvon_la, you should copy the original problem exactly, word for word, and number for number, to a post here on bitog, and then maybe someone could help you figure out how to solve it.

#### yvon_la

i am blank ! you provided me an angle that permitted me to view stuff from a different point of view but i dont know how tov fix it basicly in the tic tac toe board there can be only a/a b/b c/c but the thing i try to find work likely like this a/a/a b/b/b c/c/c so tic tac toe board doesnt work there is only 2 side usable .are there game that use tree side ( like triangular? ) tytyty ! i am further from an answer then i was but you helped me a lot fixing one huge error i hadnt notice i cant copy the original , i am doing the original!

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#### Geauxtiger

Well, I see I was no help this morning. But I also see that none of the others interpreted your question the way your meant either ( or did they?). All of follow-up answers were variations of where we started this morning.... the statistical method was essentially the same throughout the various answers. can you create a word problem that reflects what you are trying to do?

#### Tegger

Originally Posted By: yvon_la
xyz x123 y456 z789 so this would end up with 9 possibility right?
Let's see now... X has three possible states. Y has three possible states. Z has three possible states. 3 x 3 x 3 = 27 Therefore, there are 27 possible states for the combination XYZ.

#### mk378

Are you talking about not having the same character repeated adjacent? Examples: XYZ = OK XXY = NG XYX = OK XYY = NG In that case the answer is 12. The first character can be any of the three. The second one must be one of the two that don't match the first, and the third must be one of the two that don't match the second (though it doesn't matter if it matches the first). So it is 3 * 2 * 2 possible choices, resulting in 12.

#### Vikas

What in the world is "theorycrafting"? Does OP have his own language to communicate with the rest of the world?

#### yvon_la

tegger your thinking was right on the money! ty men . you got exactly my meaning! 27! dam ,i didnt expect this! now thati know the answer ! tegger ( or any other) is there a way for me to fabricate a grid or geometrical form so i can put all 27 possibility ? i was thinking of a triangle but i aint sure! ty for the help tegger you really nailed it

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