MHB Unravel the Mystery: 5 Different Rooms, 5 Different Dimensions

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Art, Ben, Cam, Dan, and Ern each added a unique room with specific dimensions. Art's room is not the shortest but shorter than at least one other room. Ben's room is one foot longer than the WORKSHOP, which is not the widest and shorter than at least one other room. The STUDY is shorter than two other rooms and narrower than Cam's room, while Dan's room is wider than the UTILITY room and not the shortest. Ern's room is longer than the widest room and shorter than at least one other room, with the DEN specifically measuring 11 feet wide. Ultimately, the clues lead to a unique identification of each room's type and dimensions.
Wilmer
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Art, Ben, Cam, Dan and Ern each added a different kind of room to his house.
Each added room can have a width of 10, 11, 12, 13 or 14 feet,
and a length (not necessarily respectively) of 15, 16, 17, 18 or 19 feet.
From the clues below, determine the kind of room each man added as well
as the width and length of each room.

1: The room Art added is not the shortest, but is shorter than at least one other room.

2: Ben's room is one foot longer than the WORKSHOP; the WORKSHOP is not the widest room,
but is shorter than at least one other room.

3: The STUDY is shorter than at least two other rooms, but not as wide as Cam's room.

4: Dan's room is not the shortest, and is wider than the UTILITY room.

5: Ern's room is longer than the length of the widest room,
and shorter than at least one other room.

6: The DEN is 11 feet wide.

7: At least two rooms are shorter than the BEDROOM.
 
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Before I lose it!
Art: bedroom, 14 by 17
Ben: den, 11 by 19
Cam: utility, 13 by 15
Dan: study, 12 by 16
Ern: workshop, 10 by 18
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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