Monday, January 20, 2014

Tuesday, December 3, 2013

Zero Factorial

I thought the following video was also worth posting because several topics show up that are relevant to College Math and Statistics, especially in one of my classes where we discussed this very question.

Connect Four

Tuesday, November 5, 2013

Murder in the Family

From Lateral Logic Puzzles by Erwin Brecher, Illus. by Lucy Corvino, Sterling Publishing Company, 1994, pg. 15-16:

There was a loud knock at the door late one Sunday evening at the home of William and Janet Garner.  William answered the door to a man who introduced himself as Detective Greg Nelson of the Los Angeles Police Department and informed William, "I'm afraid that your brother-in-law was found brutally murdered this afternoon."

William gasped.  "Oh my gosh!  Poor Ben, who could have done such a terrible thing?  My wife will be devastated."  William invited Detective Nelson inside and went to awaken his wife, Janet, who had gone to bed early with a headache.  When Janet heard the news, she became hysterical, and the doctor was called to administer a sedative.  Detective Nelson asked them to come to his office the following morning to make statements.

When William and Janet arrived at police headquarters the following morning, they were shown into Greg Nelson's office.  "Have either of you any idea as to who had a motive?" Nelson asked.  "It certainly appears that Ben knew his killer."

William looked over at Janet, "There's my sister Elizabeth's husband, Arther.  He's a really weird guy and has threatened Ben during the many arguments they've had."  Janet wiped away the tears that were rolling down her cheeks and said quietly, "There's my older brother, Peter, but he and Ben were very close.  In any case, Peter is out of town at the moment."

William leaned forward in his seat, "Of course, there is Uncle Lawrence.  He always said that Ben wished him dead so that he could get his hands on his money and he was convinced that Ben was trying to kill him.  Come to think of it, cousin Philip owed Ben a lot of money, and Ben threatened him with violence if he didn't pay up."

"I've heard enough," interjected Inspector Nelson.  "It's obvious to me that you, William Garner, committed the murder and I am placing you under arrest."

How did Inspector Nelson come to this conclusion?  

Answer after the jump.

Monday, September 23, 2013

The Banker

From Lateral Logic Puzzles by Erwin Brecher, Illus. by Lucy Corvino, Sterling Publishing Company, 1994, pg. 30:

Gerald Butcher, the London banker, was found dead in his study, slumped over the desk with a gun in his hand and a gunshot through his temple.  The blinds were drawn and the desk light was switched on.  On top of the desk was a tape recorder.

When Inspector Brown pressed the play button he heard Butcher's last message, "I cannot face the disgrace, this is the end..." then there was a gunshot.  Under the banker's head was a bloodstained letter from the Serious Fraud Office announcing an investigation into Butcher's affairs.

It seemed a clear case of suicide and the police were just about to remove the body when Inspector Brown stopped them.  "Wait a moment," he said, "this looks like murder."

What aroused his suspicion?

Answer after the jump.

Thursday, September 12, 2013

Knights and Knaves

From Mathematical Ideas 12ed. by Miller, Heeren, and Hornsby, pg. 100, #84:

In Raymond Smullyan's books, he writes about an island in which certain inhabitants are called knights and others are called knaves.  Knights always tell the truth, and knaves always lie.  Every inhabitant is either a knight or a knave.

Three inhabitants- A, B, and C- were standing together in a garden.  A stranger passed by and asked A, "Are you a knight or a knave?"  A answered, but rather indistinctly, so the stranger could not make out what he said.  The stranger then asked B, "What did A say?"  B replied, "A said that he is a knave."  At this point, the third inhabitant, C, said, "Don't believe B; he is lying!"

The question is, what are B and C?

Answer after the jump.

Thursday, September 5, 2013

Which Door?

From Mathematical Ideas 12ed. by Miller, Heeren, and Hornsby, pg. 100, #83:

In his book The Lady or the Tiger and Other Logic Puzzles, Raymond Smullyan proposes the following problem.  It is taken from the classic Frank Stockton short story, in which a prisoner must make a choice between two doors: behind one is a beautiful lady, and behind the other is a hungry tiger.

What if each door has a sign, and the man knows that only one sign is true?

The sign on Door 1 reads:
IN THIS ROOM THERE IS A LADY AND IN THE OTHER ROOM THERE IS A TIGER.

The sign on Door 2 reads:
IN ONE OF THESE ROOMS THERE IS A LADY AND IN ONE OF THESE ROOMS THERE IS A TIGER.

With this information, the man is able to choose the correct door.  Can you?

Answer after the jump.