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Touching polygons (Posted on 2013-02-27) Difficulty: 3 of 5
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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre(2): Triangular reply (partial spoilerSteve Herman2013-04-19 13:57:49
re: Triangular reply (partial spoilerJer2013-02-28 11:45:25
Hexagonal reply (partial spoiler)Steve Herman2013-02-27 23:30:17
Some ThoughtsTriangular reply (partial spoilerSteve Herman2013-02-27 23:25:23
Hints/TipsSquare reply (spoiler?)Steve Herman2013-02-27 20:28:35
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