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 Rectangles (Posted on 2018-07-03)
Subdivide the 8x10 grid below along the grid lines into nonoverlapping rectangles (some may be squares). Each rectangle must contain exactly one number; each number indicates how many small cells are contained within the rectangle.

 4 7 12 4 6 8 7 8 15 9

From Mensa Puzzle Calendar 2018 by Fraser Simpson, Workman Publishing, New York. Puzzle for June 26.

 See The Solution Submitted by Charlie No Rating

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 Solution (spoiler) Comment 1 of 1
4887777777
488CCCC466
488CCCC466
488CCCC466
7777777488
FFFFF99988
FFFFF99988
FFFFF99988

logic:
Lower 8 must be the lower of two possible positions or else 9 makes a hole.
So, 9 must be 3x3.
This allows 15 to have 5 at the bottom.
So, 6 must go exactly atop rt 8.
So, upper 7 is horizontal.
Lower 7 is horizontal flush lft., else hole.
Rt 4 descends vertically from top 7.
Finishing the top left becomes obvious.

Edited on July 4, 2018, 3:19 am
 Posted by Steven Lord on 2018-07-03 13:22:27

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