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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.'

 Submitted by Jer Rating: 4.0000 (1 votes) Solution: (Hide) 1a. 4 (in a square) 1b. 4 (as an L) 1c. 14 (surrounding an L) 2a. 6 (in a hexagon) 2b. 5 (4 in a row with the 5th out of line - 2 ways) 2c. 20 (surrounding either of the above.) 3a. 3 (in a ring) 3b. 4 (3 in a row with the 4th out of line - 2 ways) 3c. 11 (surround the more compact of the above)

 Subject Author Date re(2): Triangular reply (partial spoiler Steve Herman 2013-04-19 13:57:49 re: Triangular reply (partial spoiler Jer 2013-02-28 11:45:25 Hexagonal reply (partial spoiler) Steve Herman 2013-02-27 23:30:17 Triangular reply (partial spoiler Steve Herman 2013-02-27 23:25:23 Square reply (spoiler?) Steve Herman 2013-02-27 20:28:35

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