The following guidelines apply to all questions.

**Giza-IQ Test – Solving Guidelines**

The name of this test has nothing to do with the Egyptian pyramids. It has only to do with the fact that my name is Giulio Zambon. But it sounds exotic, doesn’t it?

The problems require the level of Math normally acquired during the first couple of years of high school, and also some knowledge of Statistics. Calculus and more advanced Math are not needed.

To answer the questions, you can use whatever resources you find appropriate, but work on your own, and avoid discussing the solutions with anybody else. Failure to do so, will sooner or later compromise the test and possibly invalidate your score.

If a numeric result has more than four digits after the decimal period, unless otherwise requested, ignore in your answer the decimal digits after the fourth one. Alternatively, when possible, you can answer with a simplified expression that, when calculated, provides the result. Radicals don’t need to be above the fraction line. For example, if you wanted to answer √3/3 to one of the questions, you could also express it as 0.5773 or 1/√3.

A fully correct answer receives a score of 1, an answer with a minor error receives a 0.75, a partly-answered question receives a 0.50, and some ideas of how a question could be answered receive a 0.25. The scorer decides how much each answer is worth, and you only get a total score.

Some of the questions are adaptations of or have been inspired by problems of the International Mathematics Olympiads. This might give a small advantage to those who took part in those contests. Nevertheless, the list of participants of each Olympiad is publicly available...

Send your answers via email to giulio(at)good(dot)at(dot)it as a list formatted more or less as follows:

1.01: answer

1.02: answer

...

Together with the list, you should provide the details of your completed and non-completed solutions. It is not strictly necessary, but it will make possible for you to get some credit for partially correct solutions. Keep the details separate from the list of answers. Append them to the email or send them as an attachment. Whatever you find most convenient.

Also, please provide the list of all I.Q. tests you have already done, each one with the result you have achieved. This will make possible to calculate the correlation between the Giza Test and the other tests.

The problems require the level of Math normally acquired during the first couple of years of high school, and also some knowledge of Statistics. Calculus and more advanced Math are not needed.

To answer the questions, you can use whatever resources you find appropriate, but work on your own, and avoid discussing the solutions with anybody else. Failure to do so, will sooner or later compromise the test and possibly invalidate your score.

If a numeric result has more than four digits after the decimal period, unless otherwise requested, ignore in your answer the decimal digits after the fourth one. Alternatively, when possible, you can answer with a simplified expression that, when calculated, provides the result. Radicals don’t need to be above the fraction line. For example, if you wanted to answer √3/3 to one of the questions, you could also express it as 0.5773 or 1/√3.

A fully correct answer receives a score of 1, an answer with a minor error receives a 0.75, a partly-answered question receives a 0.50, and some ideas of how a question could be answered receive a 0.25. The scorer decides how much each answer is worth, and you only get a total score.

Some of the questions are adaptations of or have been inspired by problems of the International Mathematics Olympiads. This might give a small advantage to those who took part in those contests. Nevertheless, the list of participants of each Olympiad is publicly available...

Send your answers via email to giulio(at)good(dot)at(dot)it as a list formatted more or less as follows:

1.01: answer

1.02: answer

...

Together with the list, you should provide the details of your completed and non-completed solutions. It is not strictly necessary, but it will make possible for you to get some credit for partially correct solutions. Keep the details separate from the list of answers. Append them to the email or send them as an attachment. Whatever you find most convenient.

Also, please provide the list of all I.Q. tests you have already done, each one with the result you have achieved. This will make possible to calculate the correlation between the Giza Test and the other tests.

And here are the first two questions:

1.01 A cone of revolution has a height that is 2/3 of the diameter of its base. Consider the largest sphere that you can fit inside the cone. What is the ratio between the volume of the sphere and the volume of the cone?

1.02 Three billiard balls rest on a table in contact with each other. A further billiard ball is placed on top of the three balls and comes therefore in contact with all three of them. Assume that none of the balls moves or rolls away when the fourth ball is put into place. If the radius of the billiard balls is 1 unit, what is the radius of the largest possible sphere that would fit in the space between the billiard balls?

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