Corpulent detective Nero Wolfe, his assistant (and unrepentant womanizer) Archie Goodwin, and Inspector Cramer of the NYPD Homicide Department were gathered in Wolfe’s office. Archie had hidden the Great Detectives: Nero Wolfe geocache but had not yet disclosed the location to the others.
You should know that Inspector Cramer always tells the truth. Archie Goodwin always lies. Nero Wolfe sometimes lies and sometimes tells the truth.
“Well, I know this much for sure,” explained Inspector Cramer. “I know the north coordinates start with 41 degrees 17 and the west coordinates start with 96 degrees 05. I just don’t know the last three digits of either longitude or latitude.”
“Let’s narrow things down,” Wolfe began. “Archie, are each of these three-digit numbers greater than 450?”
“Yes,” replied Archie.
“Are they less than 325?” asked Wolfe.
“Yes,” replied Archie.
“Now wait just a minute!” exclaimed an exasperated Cramer. “The numbers are greater than 450 and less than 325?”
“True,” replied Wolfe.
“Goodwin, does your boss always tell the truth?” asked Cramer.
“Yes,” said Goodwin.
Cramer wiped his hand down his face in frustration. “Okay, let’s simplify things. Let’s call the last three digits of the north coordinate ‘Pamela’ and the last three digits of the west coordinate ‘Gwendolyn.’ That should hold your interest, Archie.”
“Women mean nothing to me,” Archie claimed.
“Is Pamela greater than 350?” Cramer queried Goodwin.
“Yes,” Archie replied.
“Let’s see how good you are at math, Archie,” Wolfe said. “Do you know what prime numbers are?"
"No," Archie replied.
"Can you identify the first six prime numbers?" Wolfe demanded.
"No," Archie replied.
Wolfe thought for a moment. "I have added together the first six prime numbers in my head. Are Pamela's last two digits this sum?"
"No," Archie replied.
“Aha!” said Wolfe.
“Huh?” asked Cramer, bewildered.
“Now, about Gwendolyn...” Wolfe stated, glaring at his assistant. “Is her first digit an odd number?”
“Yes,” replied Archie.
“Is she smart? Would she get a perfect ACT score?”
“No,” replied Archie decisively.
“Good day, Inspector Cramer,” snarled Wolfe. “I’m sure you can show yourself out.”
“Wait a minute, Wolfe! I still don’t know where the confounded cache is!” Cramer shouted.
“We’ve given you all the information you need,” Wolfe replied. “It’s time for me to go up to the roof and attend to my orchids. And no doubt young Archie here plans to track down a real Pamela or Gwendolyn. Goodbye.”
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