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Safe Combination Possibilities 
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#1
Aug2814, 05:33 PM

P: 2

I am a 15 year old who is obsessed with math....anyway, I developed an equation dealing with safe combination possibilities. For example, if you have a safe with 5 digits, and you know there is (for example) a 4 and an 8 in the combination. You aren't sure which position they are in, and they can be rearranged in all different ways. How many possible combinations are there?
The equation i came up with was as follows: When y=total digits in the sequence and x=number of digits known, 10^(yx)y!/(yx)! will give you the answer. When you know all the digits, that's the same as saying "how many different ways can n items be arranged?" We all know that can be represented by n!, and this equation satisfies that. When you know all the numbers, 10^(yx) will cancel to 10^0, since x and y are equal. And on the bottom, (yx)! will cancel to 0!, which again is 1. Therefore you are left with y!. Also, if you know 0 of the numbers, the equation is simply 10^y, and this equation satisfies that as well. When the amount of digits you know (x) is zero, the 10^(yx) cancels to 10^y and the bottom ((yx)!) cancels to y!. There is also a y! on the top, so those cancel out and you are simply left with 10^y. So, let's say a friend hands you their phone. While trying to deduce their password, they tell you that their 4number combination contains a 3, a 6 and a 7. How many combinations are there? 10^(yx)y!/(yx)! 10^(43)4!/(43)! 10^1(24)/1! 240/1 =240 possible combinations I'm not exactly a professional mathematician (at all) but I just wanted some feedback. Are there any flaws? 


#2
Aug2814, 06:26 PM

P: 643

For the 4number code, another way, just notice that the 4th number can be any of 0,1,2,...,9 , and can be put in either in 1st, 2nd,etc. and then the other 3 numbers can be permuted, also giving 240 as result, if I understood the rules correctly. For the first, there are 5C2 ways of choosing the spots for the 4,8 , and for each of these,then the numbers in the other spots can be permutted in any way. 


#3
Aug2814, 08:23 PM

P: 643

Note that my first comment is just a joke.



#4
Aug2814, 08:24 PM

P: 2

Safe Combination Possibilities
Hahah I know:) 


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