Alpha and Betas of Mala Problem

Miss Jones has finally saved enough money to take the vacation of her dreams, a trip to Mala.  Since Miss Jones has barely enough money to take her trip, she books her own flights and arrives in Mala alone.  She is aware of the perils of touring the outback of Mala without a guide and so visits the one local tour guide agency.  As it happens, the person operating the agency is an expatriate American.  Miss Jones explains her need for a guide to the agency director.  The director then tells her, "You're in luck, I have three guides left.  I have to leave and so you may hire anyone you like.  Be careful, though.  Remember there are two cultures in Mala, the Alphas and the Betas.  The Alphas always lie.  The Betas always tell the truth.  By local custom, you may ask my group of guides only one question.  So choose wisely because you will definitely want to hire a Beta.

At this point the agency manager leaves and the three guides enter the room.  After considerable thought, Miss Jones says, "Tell me what culture you belong to."  The first man steps forward and smiles.  He then speaks in a language that Miss Jones does not understand.  At this point the second man steps forward, points to the first and says, "He says he is a Beta.  So am I."  The third man steps forward, points to the second in a very agitated manner and says, "He is lying.  He is an Alpha, the first man said he was an Alpha, and I am a Beta."

No amount of pleading can cause the guides to say more.  Who should Miss Jones hire and why?

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Alphabet Addition

DONALD + GERALD = ROBERT

There are ten different letters in this problem.  Each letter stands for a different number from 0 to 9.  You will get one hint:  D=5.  What are the correct numbers for the remaining nine letters?  If your substitutions are correct, the arithmetic in the problem will be correct.

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The Hospital Problem

Five people are in a hospital.  Each one has only one disease and each has a different disease.  Each one occupies a separate room.  The room numbers are 101-105.

  1. The person with asthma is in Room 101.

  2. Mrs. Jones has heart disease.
  3. Mrs. Green is in Room 105.
  4. Mrs. Smith has tuberculosis.
  5. The woman with mononucleosis is in Room 104.
  6. Mrs. Thomas is in Room 101.
  7. Mrs. Smith is in Room 102.
  8. One of the patients, other than Mrs. Anderson, has gall bladder disease.

What disease does each of the women have and in what room is she?

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Alpha and Beta Solution:

If Alphas always lie and Betas always tell the truth, no one would ever say "I am an Alpha."  Therefore the third man is lying and the second man telling the truth.  The first man could be either an Alpha telling a lie or a Beta telling the truth.  Miss Jones should take the sure thing and hire the second man.

Alphabet Addition Solution:  

526485 + 197485 = 723970

The Hospital Solution:

  • Mrs. Thomas, 101, asthma

  • Mrs. Smith, 102, TB
  • Mrs. Jones, 103, heart disease
  • Mrs. Anderson, 104, mono
  • Mrs. Green, 105, gall bladder disease

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