Four Girls

7th Oct 2018

In a certain, fictitious campground, a group of ten 4th grade kids and two counselors, John and Jane, were camping one weekend. That Friday night, the two counselors slept in their own separate tents while the six boys slept in one large tent and all the girls slept in another large tent.

As the night drew past midnight, John was wakened by a girl who crawled into his sleeping bag with him and kissed him. Later, she returned to the girls’ tent.

The next morning, John gathered the girls into a group by themselves and began his speech.

“Last night, one of you young ladies visited my tent. It was dark so I could not see who it was.” He looked at the girls, one by one.

Annie said, “That was Danielle.”

Danielle said, “No, it was Terri.”

Gracie said, “Well, it wasn’t me.”

Terri said, “Danielle lied when she said that it was me!”

John smiled and said, “I know you are protecting one another. And I admire that. But if only one of you is telling the truth, by deductive reasoning of what you guys have just told me, I know who it was.”

The girls looked puzzling at one another than back at John.

“Okay then. We start with Annie telling the truth and three others lying. Annie would be pointing to Danielle as my mysterious paramour. Danielle, then, would be lying. However, Terri said that Danielle lied making her statement true. Annie and Danielle would count as two true statements. So, Annie cannot be telling the truth.”

“If Danielle was telling the truth and three others lying, then it had to be Terri who kissed me last night. Terri, then, would be lying saying Danielle lied about her. But Gracie said it wasn’t her: a second true statement. Danielle cannot be telling the truth.”

“If Gracie was telling the truth, then it wasn’t her but somebody else. Annie’s statement would then have to be a lie making it impossible for my midnight lover to be Danielle. Danielle would have to be lying about it being Terri who would then be telling the truth. There you would have two truthful statements. Gracie, then lied when she said it wasn’t her who visited my bed. Which I would like to say, by the way, that our encounter was quite pleasurable and romantic but highly inappropriate in today’s society.”

Danielle frowned, “But, what if we all were telling the truth?”

John smiled and pointed, “Your statement and Terri’s statement are mutually exclusive. Only you or Terri can be telling the truth. But not both.”

Puzzled, Danielle stood frustrated. John continued. “If only one of you four lied, then three others have to be telling the truth. So then, we start with Annie lying which means it could not have been Danielle who stayed those wonderful moments with me. But we still have the Danielle and Terri logical exclusion again.”

“If Annie is the only one lying, both Danielle and Terri must be telling the truth which, as I said, only one or the other can be telling the truth. This gives rise to at least two truthful statements again, not just one. The same logic goes for just Gracie lying. Danielle and Terri gives this a problem, as well.”

“This leaves Danielle to be the only one lying and Annie truthfully saying it was Danielle who has a crush on me, Gracie insisting that it was not her, and Terri truthfully showing that Danielle was, indeed, my lover last night.”

Annie grinned, “John, doesn’t that leave just two lying and two telling the truth?”

John looked at her bright flashing eyes. “You’re a smart little girl, aren’t you? If both you and Danielle were lying, then it could have only been you that I kissed back. You and Gracie lying together is a logical impossibility, so are you and Terri lying together. If you and Danielle are both telling the truth leaving Gracie and Terri lying, then this, too, is a logical impossibility because it claims that everyone was in my tent last night. I held only one pretty little girl. The only other possibility would be if you were telling the truth, Danielle was lying, Gracie was telling the truth and Terri was lying. In that final combination, it could only have been Danielle with me last night.

Annie laughed, “There’s no way it could have been your own daughter with you?”

John looked at Terri, “No, I would have kissed her back even if it had been her.” He stared at the rest of the girls. “But from all of your statements, three liars, two liars, or just one, there is no logical way to conclude it was her.”

John waited. The four girls giggled amongst themselves. John asked, “Well?”

Terri announced, “It actually was Gracie last night, Dad. Tonight, it will be Annie’s turn and Sunday night it will be Danielle’s.”

Danielle laughed, “And Terri will visit you once you get home!”