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 Touching polygons (Posted on 2013-02-27)
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.'

 See The Solution Submitted by Jer Rating: 4.0000 (1 votes)

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 Triangular reply (partial spoiler | Comment 2 of 5 |
2a) 6, arranged in a hexagon

2b) 6.  Remove one of the 6 triangles in the hexagon, and reattach it to any triangle except the one which was directly opposite it.

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

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