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Splitting Heirs (Posted on 2005-06-15) Difficulty: 3 of 5
There was once a Duke who had an awkwardly shaped duchy, laid out like this:
       XX
 XX  XXXX
 XXXXXXX
XXXXXXXXX
XXXXXXXXX
 XX  XXXXX
 XX XXXXXX
    XXXXXX
     XXXX
     XX
Each X represents a 1000-hectare square.

The Duke was out of favor with the King, and when it came time for the Duke to pass down his land, the King hatched a plan to break up the Duke’s holdings (and thus the political power of his heirs). The King proclaimed that the Duke must split all of the land among his heirs such that:

1) The land is split into at least two pieces, and
2) Every piece has the same shape and size, allowing for rotations and/or reflections of the shape.

What are the largest pieces the Duke can break his duchy into, in accordance with the King’s edict?

No Solution Yet Submitted by Bryan    
Rating: 3.7500 (4 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsNo SubjectDustin2011-12-27 03:49:17
Some thoughts...tomarken2006-03-02 10:37:29
no subspunchmancan2005-07-29 09:27:03
Some ThoughtsGerrymander!Steve Herman2005-06-16 17:17:44
Hints/Tipsre: maximum size of possible solutionBryan2005-06-16 17:08:26
re: Solution?Gamer2005-06-15 23:38:01
SolutionSolution?sassy2005-06-15 21:36:21
Hints/Tipsmaximum size of possible solutionPaul2005-06-15 20:55:34
Another solution - 12 (A-L)Jon2005-06-15 18:09:26
Solutionsolution with 20 heirsErik O.2005-06-15 17:28:39
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