Solving for Unique Shapes on a 4x4 grid

Ravncat

New member
So - the problem is "how many unique shapes can be made by choosing 6 points on a 4x4 grid, with rotations and shifts." and then on a 3x3 grid?

I thought I could use N choose R (16 possible choices, 6 must be chosen) - no repetition - to find the number of possible combinations of points.

n!/(r!(n-r)!)

This leads to 8008 - but then I'm lost because, given a grid )A-D and 1-4

assume points

A1 A2 A3 , B1 B2 B3 are chosen - This shape is the same as points A2 A3 A4 B2 B3 B4

Likewise the shape made by A1 A2 A3, D2 D3 D4 looks the same as shape B1 C1 D1, A4 B4 C4.

I think I can just divide by 4 for the rotations - bringing me to 2002 unique shapes - but this doesn't help with duplicated shapes on transposition.

Should I be trying to do something lorenzian to find attractors? Should I just look at 3x3 permutations within the 4x4 space that would be repetitions? Since a 9 choose 6 leads to 84 - and further 21 after rotations?