Page 46 - NUMINO Challenge_D2
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Basic Concepts Color of the Hat
One of the hardest questions in logical reasoning is a question of guessing
the color of a hat that you are wearing. It is because you cannot see which
hat you are wearing while others can, and you need to observe other
people’s reactions as well as study the given conditions in order to solve the
problem.
Example A king showed one black hat and three white hats to three
prisoners, and told them that the prisoner who guessed the color
of his hat correctly would be released. Then, the king made all
three prisoners wear white hats. Each prisoner could see the hats
the others were wearing except for his. After they looked at one
another for a long time, one of the prisoners told the king that he
was wearing a white hat. Explain how the prisoner guessed the
color of his hat correctly.
Class Notes
Let three prisoners be A, B, and C.
When A looked at B and C: B and C were both wearing hats.
They stayed still because they didn’t know if they were wearing a white hat or a
black hat.
When B looked at A and C: C and A were both wearing hats.
Also, they stayed still because they didn’t know the color of their hats.
When C looked at A and B: both A and B could not tell the color of their hats because
the other two prisoners besides themselves were wearing hats.
Therefore, C realized that the color of his hat was .
43Reasoning
One of the hardest questions in logical reasoning is a question of guessing
the color of a hat that you are wearing. It is because you cannot see which
hat you are wearing while others can, and you need to observe other
people’s reactions as well as study the given conditions in order to solve the
problem.
Example A king showed one black hat and three white hats to three
prisoners, and told them that the prisoner who guessed the color
of his hat correctly would be released. Then, the king made all
three prisoners wear white hats. Each prisoner could see the hats
the others were wearing except for his. After they looked at one
another for a long time, one of the prisoners told the king that he
was wearing a white hat. Explain how the prisoner guessed the
color of his hat correctly.
Class Notes
Let three prisoners be A, B, and C.
When A looked at B and C: B and C were both wearing hats.
They stayed still because they didn’t know if they were wearing a white hat or a
black hat.
When B looked at A and C: C and A were both wearing hats.
Also, they stayed still because they didn’t know the color of their hats.
When C looked at A and B: both A and B could not tell the color of their hats because
the other two prisoners besides themselves were wearing hats.
Therefore, C realized that the color of his hat was .
43Reasoning
