Brain Teasers
Four People in a Rectangular Room
Al, Ben, Audrey, and Brenda are standing in a rectangular room. Two of them are standing at the north wall, facing south, and the other two are standing at the south wall, facing north. Two of them are standing on the west side of the room, facing each other, and the other two on the east side, facing each other. Here are some facts:
1. The tallest of the four is facing the shorter person whose name starts with the letter A.
2. The shorter male is standing diagonally across the room from the taller person whose name starts with the letter B.
3. The taller male and the shorter female are standing at the same wall.
Who is the shortest?
1. The tallest of the four is facing the shorter person whose name starts with the letter A.
2. The shorter male is standing diagonally across the room from the taller person whose name starts with the letter B.
3. The taller male and the shorter female are standing at the same wall.
Who is the shortest?
Answer
Brenda is the shortest.In the diagram below:
TS=tallest
SA=shorter person whose name starts with A
SM=shorter male
TB=taller person whose name starts with B
TM=taller female
SF=shorter female
From fact 2, we know this:
SM|
_____
|TB
From fact 1, we have the following two scenarios:
SM|
SA|
___
TS|TB
or
SM|SA
_____
|TB
|TS
Suppose scenario 1 is true. Then fact 3 tells us the room looks like this:
SM|
SA |
____
TS |TB
TM|SF
It is clear now that Al is the shorter male and the shorter person whose name starts with A. Ben is the tallest, and Brenda is the shorter female and the taller person whose name starts with B. But now Brenda is taller than Ben, the tallest of the four. So this cannot work.
This means that scenario 2 must be true. Fact 3 tells us that the room looks like this:
SM|SA
_____
SF |TB
|TS
|TM
Now it is clear that Ben is the tallest...making Al the shorter male...making Audrey the shorter person whose name starts with A...making Brenda the shorter female.
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