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Five puzzles of Oxford University that almost nobody can solve

The red and blue caps that are making people lose their heads

More and more companies look into their employees for qualities that demonstrate that they are able to solve ‘complex’ problems in the simplest way possible, universities are focused on developing and awakening them in their students; finally, it is these institutions that prepare us for professional life. In admission tests for the University of Oxford – the oldest in the UK – things are not so different.

Five of the puzzles to enter are causing much scandal since almost nobody has been able to solve them all. Apparently, the questions are too simple, but when it comes to solving them, things become complicated, so much so that the same applicators suggest looking for a quiet and comfortable place to respond correctly. Today I bring you the five riddles solved, although before reading the answer I suggest you try to solve them.

The red and blue caps that are making people lose their heads

test-acertijo-dificil

Puzzles of Oxford

Alice, Bob and Charlie are expert logicians who always tell the truth and are sitting in a row facing each other, as the picture shows. Their father puts a cap of blue or red to each one and these are the five hypothetical situations that arise, which you must solve separately (each one has its own solution).

For the five riddles, the assumption is made that Alice (sitting in the first place) can see Bob’s hat (which is sitting in the middle) and Charlie’s (who is sitting at the last) but cannot see hers. Bob can see Charlie’s hat but not his. And Charlie cannot see his hat or anybody’s hat.

These are the five riddles that are raised and which you must solve for each scenario:

  1. Their father puts a hat on each of the heads and says: “Everyone is wearing a red or blue hat. At least one of you has a red hat. “Alice says she knows the color of her hat. What color is each person’s hat?
  2. Their father puts a hat on each of his heads and says: “Everyone is wearing a red or blue hat. At least one of you has a red hat. “Alice and Bob say they do not know the color of their hats. What color is Charlie’s hat?
  3. Their father puts a hat on each of his heads and says: “Everyone is wearing a red or blue hat. At least one of you has a red hat, and at least one has a blue hat.” Alice says she knows the color of her hat and Bob says that his is red. What color is each person’s hat? 
  1. Their father puts a hat on each of his heads and says: “Everyone is wearing a red or blue hat. At least one of you has a red hat, and at least one has a blue hat.” Alice says she does not know the color of her hat, Bob says that his is red. What color is Charlie’s hat?
  2. Their father puts a hat on each of his heads and says: “Everyone is wearing a red or blue hat. Two of you, who are seated next to each other, have red hats. “Alice says she does not know the color of her hat. What color is Charlie’s hat?

Have you been able to solve them? If not, don’t worry, then I will give you the solution and an explanation of how it has been reached.

  1. If Alice says that she can know the color of her hat because she can see the color of the hat of Bob and Charlie, which are blue since only Alice can know that his hat is red because of the A condition precedent given them by his father, “At least one of you has a red hat.” So: Alice-red, Bob-blue and Charlie-blue.
  2. Charlie’s hat is red because of the condition his father gave them, “At least one of you has a red hat,” for that reason Alice and Bob cannot make a guess about the color of their own hats, since Charlie would be fulfilling the initial condition that at least one has a red hat.
  3. First Alice says that she knows the color of her hat and, due to the initial condition given to her by her father “At least one of you has a red hat, and at least one has a blue hat”, means that Bob and Charlie have the same color of hat and for that reason Alice knows that her hat must be the opposite color to fulfill the condition, upon hearing this, Bob understands what Alice says and knows that his hat is the same color as Charlie, thus, Bob’s and Charlie’s hats are red while Alice’s hat is blue.
  4. Following the initial conditions that his father gave them, “At least one of you has a red hat, and at least one has a blue hat,” if Alice cannot know what is her hat color, this means that one of those in front of her has a red hat and the other the blue one, fulfilling thus the initial condition by which Alice cannot deduce with its color, however upon hearing this, Bob understands that the color of his hat should be different than that of Charlie, for this reason, Bob concludes that his hat is red, so the color of Charlie’s hat should be blue.
  5. The initial condition that their father gave them is “Two of you, who are seated adjacent, have red hats,” if Alice does not know the color of his hat is because Bob and Charlie meets the condition of his father, both are seated adjacent and have a red hat. So Charlie has a red hat.

The explanation and the solution of the riddles are completely mine so if you detect some error or you have a different solution, do not hesitate to leave your comment.

¿Y tú qué harías?… experimentos sociales

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Acerca de Flor de Guadalupe Ortíz Gómez (125 Artículos)
Mi pasión es la ciencia, la investigación y la ingeniería pero yo siempre he pensado que eso no esta peleado con el arte, la cultura, la literatura y el pensamiento critico. Soy mexicana pero actualmente vivo en Madrid, España. Mi propósito es generar contenido interesante en Internet de una forma bien fundamentada. Contáctame para cualquier comentario o sugerencia que tengas sobre la página o si deseas que publiquemos algo en tu nombre

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