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## #1 2010-12-25 08:21:36

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Guess where this series comes from. It's hard.

0, 1, 2, 3, 4, 5, 6, 8, 9, 12.  End of Series, no more digits.
It is created from some 3-D object.
The square roots are left off because they are not needed for my purpose of size comparison.

igloo myrtilles fourmis

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## #2 2010-12-26 03:03:17

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Guess where this series comes from. It's hard.

Hint:  The object is a 3 x 3 x 3 matrix with 27 locations, looks like a rubiks cube but includes the center cube too for 27.

igloo myrtilles fourmis

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## #3 2010-12-27 08:58:12

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Guess where this series comes from. It's hard.

Hint:  We are moving around inside the object from box to box...

igloo myrtilles fourmis

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## #4 2010-12-27 18:05:46

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Guess where this series comes from. It's hard.

squares of distances avoids square rooted numbers, hence use a^2 + b^2 + c^2, where
a, b, c are either 0, 1, or 2, to indicate distance travelled.

x y z
x z y
y x z
y z x
z x y
z y x

0 0 0 = 0
0 0 1 = 1
0 1 1 = 2
1 1 1 = 3
0 0 2 = 4
0 2 1 = 5
2 1 1 = 6
0 2 2 = 8
2 2 1 = 9
2 2 2 = 12

Note for a code, you could rename 8, 9, and 12 to 7, 8, and 9, using all 10 digits.

igloo myrtilles fourmis

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