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Unreliable Witnesses (Posted on 2017-05-17) Difficulty: 3 of 5
Six witnesses gave conflicting descriptions of the suspect.

Each witness had exactly one item correct. Each correct value appears at least once.

What would be the correct description of the suspect?

Hair Jacket Shirt Pants
Brown White Red Gray
Red Blue Pink White
Black Purple Yellow Blue
Blond White Not Yellow White
Brown Purple Green Gray
Gray Blue Orange Blue

This can be solved analytically without trial and error.


From Mensa Puzzle Calendar 2017 by Mark Danna and Fraser Simpson, Workman Publishing, New York. Puzzle for May 12.

  Submitted by Charlie    
Rating: 3.6667 (3 votes)
Solution: (Hide)
Answer:
Blond hair, blue jacket, yellow shirt, gray trousers.

Each row contains exactly one correct feature, so there are six correct entries but only four columns. All the columns have at least one correct entry; the Jacket and Pants columns each must have two correct entries, as each value occurs twice. So the other two columns must have only one mention of their respective correct entries.

We thus can cross out both browns in the hair column. In the shirt column we know that yellow must be correct as "not yellow" matches any color other than yellow and there should be no double-correct in this column.

Any value that shares a row or colum with yellow can be crossed out as far as correctness goes. So any Purple jacket or Blue pants is incorrect, regardless of whether they are on the same line with yellow shirt.

Since brown hair, purple jacket and green shirt are all wrong, the fifth witness' description of Gray pants must be correct. The other witness describing gray pants must then also be correct, ruling out a white jacket, both for the first witness as well as the fourth witness. This leads to a blue jacket and then to blond hair.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
non-perfect puzzles are sometimes more interestingollie2017-05-20 05:31:02
re: Not Yellow ShirtSteve Herman2017-05-18 15:43:56
QuestionNot Yellow Shirtatheron2017-05-18 15:06:11
SolutionAnalytical Solution (Spoiler)Steve Herman2017-05-17 10:50:10
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