# What's the chance that this happens?

#### Eleredo

##### Member
What's the chance that some person will ever solve the same 7x7x7 scramble as another person? (apart from scrambles that are posted to solve, or at competitions of course)

I think it never happens, and that every scramble is unique.
There are way too many combinations for that to happen.

@5BLD: Well, what I meant is how likely it would be for two people to have the same scramble.

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#### Tao Yu

##### Member
There are more different 7x7 scrambles than there are atoms in the universe.
Everytime you scramble a 7x7, be proud . Only you have ever scrambled it into that position(Unless you are really,really,really,really,really unlucky)

I think the chance is 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692 043 434 567 152 132 912 323 232 706 135 469 180 065 278 712 755 853 360 682 328 551 719 137 311 299 993 600 000 000 000 000 000 000 000 000 000 000 000^2

Am I wrong?

edit:no ^2

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#### Godmil

Tao, if that big number is the number of possible permutations, then the probability of doing the same solve (I'd guess) is just one in that number.... since the first person has nothing special about their scramble there is no probability associated with it (other than 1), so the second person has a 1 in xxxxxxxx chance of having the same one.

#### Tao Yu

##### Member
Tao, if that big number is the number of possible permutations, then the probability of doing the same solve (I'd guess) is just one in that number.... since the first person has nothing special about their scramble there is no probability associated with it (other than 1), so the second person has a 1 in xxxxxxxx chance of having the same one.
Oh right, I suck at probablity

#### 5BLD

##### Member
Solve?
There is an infinite number of ways to solve a given scramble, if you think of it mathematically. However, if we factored in the maximum number of turns that are likely, etc. You could work it out.
Yes, I'm too lazy to do the maths.

#### aaronb

##### Member
Assuming no one has ever done the same scramble before, it's

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
1.95*10^160

or

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
19,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000

Edit:
My guess is that anyone who has done a 7x7 solve combined have probably done a total of around 50,000 to 100,000 solves/scrambles. So the answer to your question could be about :

100,000
------------------------------------------------------------
19,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000

or

1
------------------------------------------------------------
195,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000

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#### Tyjet66

##### Member
Assuming no one has ever done the same scramble before, it's

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
1.95*10^160

or

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
19,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000

Edit:
My guess is that anyone who has done a 7x7 solve combined have probably done a total of around 50,000 to 100,000 solves/scrambles. So the answer to your question could be about :

100,000
------------------------------------------------------------
19,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000

or

1
------------------------------------------------------------
195,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000
In other words, damn near impossible.

#### luke1984

##### Member
If you would have as many 7x7x7 cubes as there are possible permutations on that puzzle, you could fill the entire visible universe with 7x7x7s.

#### Lucas Garron

##### Member
Probably the likelihood that CCT or PPT have the same random seed for 7x7x7 some time.

#### Carson

Is this for the exact same SCRAMBLE or PERMUTATION? It is possible to get the same cube state from multiple scrambles.

#### 5BLD

##### Member
What's the chance that some person will ever solve the same 7x7x7 scramble as another person? (apart from scrambles that are posted to solve, or at competitions of course)

I think it never happens, and that every scramble is unique.
There are way too many combinations for that to happen.

@5BLD: Well, what I meant is how likely it would be for two people to have the same scramble.
Ah, same scramble. Yes it took my this long to read your edit.
Then I'm not sure. i.e. I'm too lazy to calculate it.