# God's number proven at 20

#### guysensei1

##### Member
Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and iff you own a calculator, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
You think it's possible to check all the 20 move Algs 'with a calculator'?

#### Christopher Mowla

Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and iff you own a calculator, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
That's a good question, but you have to realize two things:
[1] The number of algorithms drastically increases as the move length increases. So there are A LOT more 15 move algorithms than 14 move algorithms, for example.
[2] We do not have enough memory to store/keep track of all unique positions reached with each move sequence.

As far as what you quoted penfold1992 saying, I agree. It would be much more satisfying if this was proved without brute force.

#### qqwref

##### Member
Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and iff you own a calculator, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
Do you have any idea how much 43 quintillion is? It's 43 million million million.

Have fun doing it by hand on a calculator. I'll see you in a couple of million million years.

#### Cube Is Life

##### Member
Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and iff you own a calculator, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
You can't count the same cube twice and some 6 move algs give you the same cube as some 0 move algs. So the super computer had to figure out wich ones will give you unique cubes.

#### WinPooh

##### Member
Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and iff you own a calculator, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
You need to store some information about seen positions somewhere. Even 1 bit per position x 43 quintillion will require very large storage...
43 * 10^18 bit = 5 * 10^18 bytes
Lets use terabyte hard drives (10^12 bytes each). We need 43 000 000 discs. Maybe Google does have 43 million HDDs, but I doubt there exist any manager in Google who will approve using them for such task

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#### Tony Fisher

##### Member
Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and if you own a computer, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
I love the way you say "it shouldn't be too hard". Perhaps for the 4x4x4 they will ask you how to do it. 43 quintillion is a very big number and it's not as if it has to 'just' do that number of straight calculations. It would need to run a program that did various things like check for repeated positions and know how to actually go through all the moves of each set of algs.

#### LNZ

According to people who actually do such calculations, there are about 490 million depth 20 positions in HTM.

#### elrog

##### Member
Can't you just do all the different 1 move algs, then all the 2 move algs, then all the three move algs, etc. until you reach 43 quintillion, and if you own a computer, it shouldn't be too hard, so why did it take some google supercomputers to work it out?
When I was relatively new, I asked a very similar question. I will do my best to explain why this doesn't work.

If you add up every possible 1 move alg, 2 move alg, and so on, you will reach 43 quintillion after 18 moves. The reason for this is that a 15 move alg may solve the same position of a 7 move alg you already counted earlier, so reaching 43 quintillion algs isn't the same as reaching 43 quintillion states. To filter through the states you have already counted, you would need a database of every possible state. This would take a lot of storage space and you would need a million million years (as previously stated) to sort through it.

And just for you information, this is how the lower bound of 18 moves was established.