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Liar Playing Spitball (Posted on 2022-08-17) Difficulty: 3 of 5
It was the last class of the afternoon and Mrs. Nesbitt was reading a book as her seventh grade algebra class finished it's homework. Being engrossed in her reading, she had her nose buried in the book. All of a sudden, from the right-hand side of the room, a big, well-constructed spitball sailed past her head and slapped against the blackboard behind her.

Glancing up startled, she could only tell that it had come from the row closest to the window or the row immediately inside of that. Also from the angle, it appeared to come from the front half of one of these rows. All the students were deeply engrossed in their work and no one was looking up from that side of the room. From the other side of the room, however it was a different story.

Several students were looking around with a grin on their faces as if they had seen the whole thing. But of course, no one would admit to anything. So Mrs. Nesbitt was left to discover the culprit herself. She narrowed the field of possible delinquents to four students and began to question them. She asked, "Who threw this spitball?" Each of the four students made one statement:
  1. Mary Abramson: I didn't do it.
  2. Nathan Jackson: I didn't do it.
  3. Mark Martin: Abramson did it
  4. Lu Ann Blanchard: Mark is telling the truth.
Being a very clever teacher, Mrs. Nesbitt knew that only two students were telling the truth. So, she questioned them again. She asked again, "Who threw that spitball?" Again each student made one statement.
  1. Mary Abramson: Lu Ann did it.
  2. Nathan Jackson: Martin didn't do it.
  3. Mark Martin: Blanchard didn't do it.
  4. Lu Ann Blanchard: Mary is lying.
"Now this is interesting," thought Mrs. Nesbitt, "Each student who lied earlier has told the truth, and each one who told the truth has now lied! Oh well, no matter, I know who the culprit is!"

Determine the culprit from the clues provided above.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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  Subject Author Date
solnSteven Lord2022-08-17 09:10:52
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