Heap, Egyptian Equation

What may be the earliest note of an equation is found in the ancient Egyptian records of Ahmes in the following form: “heap, its two-thirds, its half, its seventh, its whole gives 97.” If we interpret “its two-thirds” as “two thirds of the heap” and assume that we are adding all of these amounts, we can find out how big the heap is. Proceed.

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Highland Island 2 (C, P)

Back on Highland Island once again, you are out for a walk (you take a lot of walks), and you encounter three of the natives. You can’t tell whether each of them is a Chocolate (truth teller) or a Peach (liar). Forgetting that this won’t help you, you ask the first native what he is. He mumbles something that you can’t hear. The second native says, “He says he’s a Chocolate. He is one and I am too.” The third native speaks up immediately: “That’s not true. The first guy is a Peach, and I’m a Chocolate.” Who is what?

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Soccer Game Scores 1

Three soccer teams, A, B, and C, all play each other one game. Most of the data from the three games was lost by a careless clerk, including the score of each match. You, as sports editor, are alone in the copy room of the newspaper and must write up the scores of the games. Due to a sudden storm, telephone lines are down and so you will have to figure out these scores from the one piece of paper that the clerk did manage to get to you—and even IT has some figures missing. Use this sketchy information to figure out the scores of the three soccer games.

  played won lost tied goals for
(2-game total)
goals against
(2-game total)
A 2 1 ? ? 4 ?
B 2 ? ? ? 3 0
C 2 ? ? 1 2 ?

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Hospital Staff (Doctors, Nurses)

A staff member of a small hospital said, “The hospital staff consists of 16 doctors and nurses, including me. The following facts apply to the staff members; whether you include me or not does not make any difference.”

The staff consists of:

  1. more nurses than doctors;
  2. more male doctors than male nurses;
  3. more male nurses than female nurses;
  4. at least one female doctor.

Give the sex and job of the speaker.

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Cube With 6 Cuts

A cube is made from a block of white pine, 6 cm on each edge. It is painted a nice barn red. After the paint dries, the cube is cut into 27 little cubes, each one 2 cm on each edge. This can be done with six cuts of the saw, right? Now, a question: Starting over, after making a saw cut, you are allowed to rearrange the pieces any way you want before making the next cut. Following this rule, can you make the 27 little cubes in fewer than six cuts of the saw?

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