1a. What is the least number of identical squares that can be placed in a plane such that each shares a side with exactly two others?

1b. What is the least number of identical squares that can be placed in a plane such that each shares a side with at least one other and they form a contiguous region with no rotation or reflection symmetry?

1c. What is the least number of identical squares that can be placed in a plane such that each shares a side with exactly two others and they form a contiguous region with no rotation or reflection symmetry?

2a-c. Same as 1a-c. but replace 'squares' with 'equilateral triangles.'

3a-c. Same as 1a-c. but replace 'squares' with 'regular hexagons.'

2a) 6, arranged in a hexagon

Posted by Steve Herman on 2013-02-27 23:25:23